Multiple ChoiceGiven the functions h(x)=2x3−4h\left(x\right)=2x^3-4h(x)=2x3−4 and k(x)=x2+2k\left(x\right)=x^2+2k(x)=x2+2, find and fully simplify h⋅k(x)h\cdot k\left(x\right)h⋅k(x)124viewsHas a video solution.
Multiple ChoiceGiven the functions L(x)=x−2L\left(x\right)=x-2L(x)=x−2 and M(x)=x2M\left(x\right)=x^2M(x)=x2, calculate LM(5)\frac{L}{M}\left(5\right)ML(5)143views2rankHas a video solution.
Textbook QuestionWithout using paper and pencil, evaluate each expression given the following functions. ƒ(x)=x+1 and g(x)=x^2 (ƒ+g)(2)125viewsHas a video solution.
Textbook QuestionWithout using paper and pencil, evaluate each expression given the following functions. ƒ(x)=x+1 and g(x)=x^2 (ƒ/g)(2)141viewsHas a video solution.
Textbook QuestionIn Exercises 1–30, find the domain of each function. f(x) = x² - 2x - 15174viewsHas a video solution.
Textbook QuestionLet ƒ(x)=x^2+3 and g(x)=-2x+6. Find each of the following. See Example 1. (ƒ+g)(3)139viewsHas a video solution.
Textbook QuestionLet ƒ(x)=x^2+3 and g(x)=-2x+6. Find each of the following. See Example 1. (ƒ-g)(-1)142viewsHas a video solution.
Textbook QuestionIn Exercises 1–30, find the domain of each function. f(x) = 1/[3/(x - 1) - 2]166viewsHas a video solution.
Textbook QuestionLet ƒ(x)=x^2+3 and g(x)=-2x+6. Find each of the following. See Example 1. (ƒ/g)(-1)178viewsHas a video solution.
Textbook QuestionFor the pair of functions defined, find (f/g)(x).Give the domain of each. See Example 2. ƒ(x)=3x+4, g(x)=2x-8159viewsHas a video solution.
Textbook QuestionFor the pair of functions defined, find (ƒ+g)(x).Give the domain of each. See Example 2. ƒ(x)=3x+4, g(x)=2x-5160viewsHas a video solution.
Textbook QuestionFor the pair of functions defined, find (ƒ-g)(x). Give the domain of each. See Example 2. ƒ(x)=2x^2-3x, g(x)=x^2-x+3158viewsHas a video solution.
Textbook QuestionFor the pair of functions defined, find (ƒ+g)(x). Give the domain of each. See Example 2. ƒ(x)=√(4x-1), g(x)=1/x249viewsHas a video solution.
Textbook QuestionIn Exercises 1–30, find the domain of each function. h(x) = √(x −2)+ √(x +3)141viewsHas a video solution.
Textbook QuestionIn Exercises 31–50, find fg and determine the domain for each function. f(x) = x -5, g(x) = 3x²280viewsHas a video solution.
Textbook QuestionUse the graph to evaluate each expression. See Example 3(a). (ƒ+g)(2) 142viewsHas a video solution.
Textbook QuestionIn Exercises 31–50, find f−g and determine the domain for each function. f(x) = x -5, g(x) = 3x²184viewsHas a video solution.
Textbook QuestionUse the graph to evaluate each expression. See Example 3(a). (ƒ-g)(-1) 128viewsHas a video solution.
Textbook QuestionIn Exercises 31–50, find ƒ/g and determine the domain for each function. f(x) = 2x² − x − 3, g (x) = x + 1147viewsHas a video solution.
Textbook QuestionIn Exercises 31–50, find ƒ+g and determine the domain for each function. f(x) = 2x² − x − 3, g (x) = x + 1144viewsHas a video solution.
Textbook QuestionIn Exercises 31–50, find ƒ+g and determine the domain for each function. f(x) = 3 − x², g(x) = x² + 2x − 15170viewsHas a video solution.
Textbook QuestionIn Exercises 31–50, find fg and determine the domain for each function. f(x) = √x, g(x) = x − 4158viewsHas a video solution.
Textbook QuestionIn Exercises 31–50, find f/g and determine the domain for each function. f(x) = 2 + 1/x, g(x) = 1/x142viewsHas a video solution.
Textbook QuestionFor each function, find (a)ƒ(x+h), (b)ƒ(x+h)-ƒ(x), and (c)[ƒ(x+h)-ƒ(x)]/h.See Example 4. ƒ(x)=2-x150viewsHas a video solution.
Textbook QuestionIn Exercises 31–50, find fg and determine the domain for each function. f(x)= = 8x/(x - 2), g(x) = 6/(x+3)146viewsHas a video solution.
Textbook QuestionIn Exercises 31–50, find ƒ+g and determine the domain for each function. f(x)= = 8x/(x - 2), g(x) = 6/(x+3)143viewsHas a video solution.
Textbook QuestionFor each function, find (a)ƒ(x+h), (b)ƒ(x+h)-ƒ(x), and (c)[ƒ(x+h)-ƒ(x)]/h.See Example 4. ƒ(x)=1/x149viewsHas a video solution.
Textbook QuestionIn 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)151viewsHas a video solution.
Textbook QuestionFor each function, find (a)ƒ(x+h), (b)ƒ(x+h)-ƒ(x), and (c)[ƒ(x+h)-ƒ(x)]/h.See Example 4. ƒ(x)=x^2131viewsHas a video solution.
Textbook QuestionFor each function, find (a)ƒ(x+h), (b)ƒ(x+h)-ƒ(x), and (c)[ƒ(x+h)-ƒ(x)]/h.See Example 4. ƒ(x)=1+2x^2156viewsHas a video solution.
Textbook QuestionIn Exercises 51–66, find a. (fog) (x) b. (go f) (x) f(x)=4x-3, g(x) = 5x² - 2168viewsHas a video solution.
Textbook QuestionFor each function, find (a)ƒ(x+h), (b)ƒ(x+h)-ƒ(x), and (c)[ƒ(x+h)-ƒ(x)]/h.See Example 4. ƒ(x)=x^2-4x+2152viewsHas a video solution.
Textbook QuestionIn Exercises 51–66, find a. (fog) (2) b. (go f) (2) f(x) = 4-x, g(x) = 2x² +x+5164viewsHas a video solution.
Textbook QuestionLet ƒ(x)=2x-3 and g(x)=-x+3. Find each function value. See Example 5. (g∘ƒ)(0)177viewsHas a video solution.
Textbook QuestionLet ƒ(x)=2x-3 and g(x)=-x+3. Find each function value. See Example 5. (g∘g)(-2)149viewsHas a video solution.
Textbook QuestionIn 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/x160viewsHas a video solution.
Textbook QuestionGiven functions f and g, find (a)(ƒ∘g)(x) and its domain. See Examples 6 and 7. ƒ(x)=8x+12, g(x)=3x-1194viewsHas a video solution.
Textbook QuestionGiven functions f and g, find (a)(ƒ∘g)(x) and its domain. See Examples 6 and 7. ƒ(x)=√x, g(x)=x+3147viewsHas a video solution.
Textbook QuestionIn Exercises 75-82, express the given function h as a composition of two functions ƒ and g so that h(x) = (fog) (x). h(x) = (3x − 1)^4238viewsHas a video solution.
Textbook QuestionGiven functions f and g, (b)(g∘ƒ)(x) and its domain. See Examples 6 and 7. ƒ(x)=x^3, g(x)=x^2+3x-1194viewsHas a video solution.
Textbook QuestionGiven functions f and g, find (b)(g∘ƒ)(x) and its domain. See Examples 6 and 7. ƒ(x)=x+2, g(x)=x^4+x^2-4169viewsHas a video solution.
Textbook QuestionGiven functions f and g, find (b)(g∘ƒ)(x) and its domain. See Examples 6 and 7. ƒ(x)=√(x-1), g(x)=3x230viewsHas a video solution.
Textbook QuestionUse the graphs of f and g to solve Exercises 83–90. Find (g-f) (-2).228viewsHas a video solution.
Textbook QuestionGiven functions f and g, find (a)(ƒ∘g)(x) and its domain. See Examples 6 and 7. ƒ(x)=√x, g(x)=1/(x+5)130viewsHas a video solution.
Textbook QuestionIn Exercises 87–88, find a. (f ○ g)(x); b. the domain of (f ○ g). f(x) = (x + 1)/(x - 2), g(x) = 1/x236viewsHas a video solution.
Textbook QuestionUse the graphs of f and g to solve Exercises 83–90. Graph f+g.141viewsHas a video solution.
Textbook QuestionUse the graphs of f and g to solve Exercises 83–90. Graph f-g.399viewsHas a video solution.
Textbook QuestionLet ƒ(x) = √(x-2) and g(x) = x^2. Find each of the following, if possible. (g ○ ƒ)(x)135viewsHas a video solution.
Textbook QuestionLet ƒ(x) = √(x-2) and g(x) = x^2. Find each of the following, if possible. (g ○ ƒ)(3)138viewsHas a video solution.
Textbook QuestionUse the table to evaluate each expression, if possible. (ƒ+g)(1)163viewsHas a video solution.
Textbook QuestionUse the table to evaluate each expression, if possible. (f/g) (0)185viewsHas a video solution.
Textbook QuestionThe graphs of two functions ƒ and g are shown in the figures. Find (ƒ∘g)(2).149viewsHas a video solution.