College Algebra

In Exercises 27–38, evaluate each function at the given values of the independent variable and simplify. f(x) = |x+3|/|x + 3| b. f(-5)

In Exercises 11–26, determine whether each equation defines y as a function of x. y = - √x +4

In Exercises 27–38, evaluate each function at the given values of the independent variable and simplify. f(r) = √(r + 6) +3 c. f(x-6)

In Exercises 11–26, determine whether each equation defines y as a function of x. y = √x +4

In Exercises 27–38, evaluate each function at the given values of the independent variable and simplify. f(r) = √(r + 6) +3 b. f(10)

In Exercises 11–26, determine whether each equation defines y as a function of x. x + y = 16

In Exercises 27–38, evaluate each function at the given values of the independent variable and simplify. h(x) = x^4 - x²+1 d. h (3a)

In Exercises 1–10, determine whether each relation is a function. Give the domain and range for each relation. {(1, 4), (1, 5), (1, 6)}

In Exercises 27–38, evaluate each function at the given values of the independent variable and simplify. h(x) = x^4 - x²+1 c. h (-x)

In Exercises 1–10, determine whether each relation is a function. Give the domain and range for each relation. {(-3, -3), (-2, −2), (−1, −1), (0, 0)}

In Exercises 27–38, evaluate each function at the given values of the independent variable and simplify. f(x) = |x+3|/|x + 3| c. f(−9 - x)

In Exercises 1–10, determine whether each relation is a function. Give the domain and range for each relation. {(3, −2), (5, −2), (7, 1), (4, 9)}

In Exercises 27–38, evaluate each function at the given values of the independent variable and simplify. h(x) = x³ − x + 1 d. h (3a)

In Exercises 1–10, determine whether each relation is a function. Give the domain and range for each relation. {(3, 4), (3, 5), (4, 4), (4, 5)}

In Exercises 27–38, evaluate each function at the given values of the independent variable and simplify. h(x) = x³ − x + 1 c. h (-x)

In Exercises 1–10, determine whether each relation is a function. Give the domain and range for each relation.{(1, 2), (3, 4), (5, 5)}

Simplify: 2(x+h)² + 3 (x + h) + 5 − (2x² + 3x + 5).

Determine whether the graph of each equation is symmetric with respect to the y-axis, the x-axis, the origin, more than one of those, or none of these. x^2 + y^2 =17

In Exercises 95–96, let f and g be defined by the following table: Find |ƒ(1) − f(0)| − [g (1)]² +g(1) ÷ ƒ(−1) · g (2) .

Evaluate each function at the given values of the independent variable and simplify. g(x) = 3x^2 - 5x + 2 (a) g(0), (b) g(-2), (c) g(x-1), (d) g(-x)

In Exercises 95–96, let f and g be defined by the following table: Find √(ƒ(−1) − f(0)) – [g (2)]² + ƒ(−2) ÷ g (2) · g (−1) .

Determine whether each equation defines y as a function of x. 2x + y^2 = 6

In Exercises 93-94, let f(x) = x² − x + 4 and g(x) = 3x – 5. Find g(-1) and f(g(-1)).

Determine whether each equation defines y as a function of x. 2x + y = 8

In Exercises 93-94, let f(x) = x² − x + 4 and g(x) = 3x – 5. Find g (1) and f(g(1)).

Determine whether each relation is a funciton, Give the domain and range for each relation. (1, 10), (2, 500), (13, π)

In Exercises 27–38, evaluate each function at the given values of the independent variable and simplify. f(x) = |x+3|/|x + 3| a. f(5)

In Exercises 11–26, determine whether each equation defines y as a function of x. x+y³ = 8

In Exercises 41–44, use the given conditions to write an equation for each line in point-slope form and slope-intercept form. Passing through (-3, 6) and perpendicular to the line whose equation is y = (1/3)x + 4

In Exercises 41–44, use the given conditions to write an equation for each line in point-slope form and slope-intercept form. Passing through (4, -7) and parallel to the line whose equation is 3x + y - 9 = 0.

In Exercises 41–44, use the given conditions to write an equation for each line in point-slope form and slope-intercept form. Passing through (-3, 2) with slope - 6

In Exercises 37–40, find the slope of the line passing through each pair of points or state that the slope is undefined. Then indicate whether the line through the points rises, falls, is horizontal, or is vertical. (-1, -2) and (-3, -4)

In Exercises 33–34, find and simplify the difference quotient [f(x + h) - f(x)]/h, h =/= 0 for the given function. f(x) = -2x^2 + x + 10

Find the average rate of change of f(x) = x^2 - 4x from x_1 = 5 to x_2 = 9.

In Exercises 31–50, find fg and determine the domain for each function. f(x) = 2x² − x − 3, g (x) = x + 1

In Exercises 31–50, find f/g and determine the domain for each function. f(x) = 2x + 3, g(x) = x − 1

In Exercises 67-74, find a. (fog) (x) b. the domain of f o g. f(x) = x² + 4, g(x) = √(1 − x)

In Exercises 51–66, find a. (fog) (x) b. (go f) (x) c. (fog) (2) d. (go f) (2). f(x) = 2x-3, g(x) = (x+3)/2

In Exercises 31–50, find ƒ+g and determine the domain for each function. f(x) = √(x +4), g(x) = √(x − 1)

In Exercises 1–30, find the domain of each function. h(x) = 4/(3/x - 1)

In Exercises 1–30, find the domain of each function. g(x) = 2/(x+5)

In Exercises 76–81, find the domain of each function. f(x) = x/(x^2 + 4x -21)

In Exercises 31–50, find f−g and determine the domain for each function. f(x) = 2x² − x − 3, g (x) = x + 1

In Exercises 31–50, find fg and determine the domain for each function. f(x) = 2x + 3, g(x) = x − 1

In Exercises 67-74, find a. (fog) (x) b. the domain of f o g. f(x) = √x, g(x) = x − 2

In Exercises 51–66, find c. (fog) (2) d. (go f) (2). f(x) = √x, g(x) = x − 1

In Exercises 31–50, find ƒ+g and determine the domain for each function. f(x) = x -5, g(x) = 3x²

In Exercises 1–30, find the domain of each function. f(x) = 1/(x^2+1) - 1/(x^2-1)

In Exercises 1–30, find the domain of each function. f(x)=3(x-4)

In Exercises 76–81, find the domain of each function. g(x) = 4/(x - 7)

In Exercises 31–50, find f/g and determine the domain for each function. f(x) = x -5, g(x) = 3x²

In Exercises 31–50, find f−g and determine the domain for each function. f(x) = 2x + 3, g(x) = x − 1

In Exercises 67-74, find a. (fog) (x) b. the domain of f o g. f(x) = x/(x+1), g(x) = 4/x

In Exercises 51–66, find a. (fog) (x) b. (go f) (x) f(x) = 4-x, g(x) = 2x² +x+5

In Exercises 31–50, find ƒ+g and determine the domain for each function. f(x) = 2x + 3, g(x) = x − 1

In Exercises 1–30, find the domain of each function. f(x) = 1/(x+7) + 3/(x-9)

In Exercises 89–90, express the given function h as a composition of two functions f and g so that h(x) = (f ○ g)(x). h(x) = (x^2 + 2x - 1)^4

In Exercises 31–50, find fg and determine the domain for each function. f(x) = x -5, g(x) = 3x²

Solve and check: (x-1)/5 - (x+3)/2 = 1- x/4

In Exercises 67-74, find a. (fog) (x) b. the domain of f o g. f(x) = 2/(x+3), g(x) = 1/x

In Exercises 51–66, find a. (fog) (x) b. (go f) (x) f(x)=4x-3, g(x) = 5x² - 2

In Exercises 1–30, find the domain of each function. f(x) = √(x - 3)

In Exercises 1–30, find the domain of each function. g(x) = 3/(x^2-2x-15)

In Exercises 87–88, find a. (f ○ g)(x); b. the domain of (f ○ g). f(x) = (x + 1)/(x - 2), g(x) = 1/x

In Exercises 31–50, find f−g and determine the domain for each function. f(x) = x -5, g(x) = 3x²

In Exercises 95–96, find all values of x satisfying the given conditions. f(x) = 2x − 5, g(x) = x² − 3x + 8, and (ƒ o g) (x) = 7.

In Exercises 51–66, find a. (fog) (x) b. (go f) (x) c. (fog) (2) d. (go f) (2). f(x) = 1/x, g(x)= 1/x

In Exercises 31–50, find ƒ+g, f−g, fg, and f/g. Determine the domain for each function. f(x) = √(x -2), g(x) = √(2-x)

In Exercises 1–30, find the domain of each function. f(x) = 1/[3/(x - 1) - 2]

In Exercises 1–30, find the domain of each function. f(x) = x² - 2x - 15

In Exercises 82–84, find f + g, f - g, fg, and f/g. f(x) = x^2 + x + 1, g(x) = x^2 -1

The functions in Exercises 93–95 are all one-to-one. For each function, (a) find an equation for f^(-1)x, the inverse function. (b) Verify that your equation is correct by showing that f(f^(-1)(x)) = x and f^(-1)(f(x)) = x. f(x) = (x - 7)/(x + 2)

The functions in Exercises 93–95 are all one-to-one. For each function, (a) find an equation for f^(-1)x, the inverse function. (b) Verify that your equation is correct by showing that f(f^(-1)(x)) = x and f^(-1)(f(x)) = x. f(x) = 4x - 3

In Exercises 109–111, give the center and radius of each circle. x^2 + y^2 - 4x + 2y - 4 = 0

In Exercises 107–108, write the standard form of the equation of the circle with the given center and radius. Center (-2. 4), r = 6

In Exercises 105–106, find the midpoint of each line segment with the given endpoints. (2, 6) and (-12, 4)