They are not inverses because $$f(g(x)) \neq x$$

Question 1

Solve the absolute value equation $$|6 - 5x| = 2. $$What are the solutions?

Accepted Answer

Question 2

Solve the quadratic equation $$x^2 + 5x - 36 = 0$ by completing the square.

Accepted Answer

$$x = 4 or$$ $$x = -9$$

Question 3

Which of the following is the correct standard form equation for a circle with center $$(-1, 1)$$ and radius $$2$$?

Accepted Answer

$$(x + 1)^2$ + (y - 1)^2$ = 4$$

Question 4

Given the function $$f(x) = -5x + 6$$, what is $$f(x+2)$$?

Accepted Answer

$$-5x - 4$$

Question 5

Find the $$x-$$intercept of the line $$7x + 2y = 14.$$

Accepted Answer

$$(2, 0)$$

Question 6

Which of the following relations is NOT a function?

Accepted Answer

{$$(3, 2), (4, 2), (3, 3)$$}

Question 7

Let $$f(x) = x^2$ - 4$$ and $$g(x) = 5 - x. $$Find $$(fg)(-6).$$

Accepted Answer

$$352$$

Question 8

For the ellipse $$\frac{x^2$}{81} + \frac{y^2$}{64} = 1$$, what are the coordinates of the foci?

Accepted Answer

$$(\pm \sqrt{81 - 64}, 0)$$

Question 9

Solve the system of equations: $$3x + y = 18$$, $$y = 3x. $$What is the solution?

Accepted Answer

$$(3, 9)$$

Question 10

Which of the following statements is true about the function $$f(x) = 2x + 6$$ and $$g(x) = x^2$ + 3$$?

Accepted Answer

They are not inverses because $$f(g(x)) 
eq x$$

Question 11

What is the solution to the equation $$16^x = 4$$?

Accepted Answer

$$x = \frac{1}{2}$$

Question 12

Use the change-of-base formula to evaluate $$\log_2$ 5 to $$four decimal places.

Accepted Answer

$$2.3219$$

Question 13

Which of the following must be true for a function to have an inverse?

Accepted Answer

It must be one-to-one

Question 14

Given the system $$\begin{cases} 5x - y = 24 \ x + 9y = 14 \end{cases}$$, solve by elimination.

Accepted Answer

$$(5, -1)$$

Question 15

What is the vertex of the quadratic function $$f(x) = x^2$ - 12x + 32$$?

Accepted Answer

$$(6, -4)$$

Question 16

Which of the following is the correct equation of the asymptotes for the hyperbola $$\frac{y^2$}{225} - \frac{x^2$}{64} = 1$$?

Accepted Answer

$$y = \pm \frac{15}{8}x$$

Question 17

If $$f(x) = 2^x$$, what is $$f(3) + f(-3)$$?

Accepted Answer

$$8.125$$

Question 18

Given the system $$\begin{cases} 3x + 5y = 13 \ x + y = 9 \end{cases}$$, what is the value of $$y in $$the solution $$(4, y)$$?

Accepted Answer

$$5$$

Question 19

Which of the following is the correct exponential form for $$\log_4$(x) = 3$$?

Accepted Answer

$$4^3 = x$

Question 20

What is the midpoint between the points $$(11, 1)$$ and $$(6, 10)$$?

Accepted Answer

$$(8.5, 5.5)$$

College Algebra Final Review – Step-by-Step Study Guidance

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