Question 1

Simplify the expression $$\frac{-36x$$^{13}$$y^{13}z^7$}{4x^8$y^6z^6$}$$ and choose the correct answer.

Accepted Answer

$$-9x^5y^7$z$

Question 2

A biologist is modeling population growth using the function $$f(x) = 4x - 8. $$What is the inverse function $$f^{-1}(x$$)$$?

Accepted Answer

$$f^{-1}(x$$) = \frac{x + 8}{4}$$

Question 3

Simplify $$(2x^3y^4$/z^4)^2$ and select the correct answer.

Accepted Answer

$$4x^6y^8$/z^8$$

Question 4

A pharmaceutical company uses the function $$f(x) = \sqrt{x + 4} to $$model the concentration of a drug. What is the inverse function $$f^{-1}(x$$)$$?

Accepted Answer

$$f^{-1}(x$$) = $$x^2 - 4$

Question 5

Perform the operation and write the resulting polynomial in standard form: $$(8x^6$$ - $$8x^5$$ - $$4x^4 - 1$$) - $$(5x^6$$ - $$3x^5$$ + $$6x^4 + 3$$)$$.

Accepted Answer

$$3x^6$$ - $$5x^5$$ - $$10x^4 - 4$

Question 6

Find the product $$(x - 12)(x^2$ + 4x - 7)$$ and select the correct answer.

Accepted Answer

$$x^3$$ - $$8x^2 - 55x + 84$

Question 7

Let $$f(x) = 9x - 6$$ and $$g(x) = 4x - 8. $$What is the domain of $$\frac{f(x)}{g(x)} in $$interval notation?

Accepted Answer

$$(-\infty, 2) \cup (2, \infty)$$

Question 8

Let $$f(x) = 5x + 9$$ and $$g(x) = 9x - 6. $$What is $$(f \cdot g)(x)$$?

Accepted Answer

$$45x^2 + 51x - 54$

Question 9

Find the inverse of $$f(x) = \frac{7x - 1}{6}$$ and select the correct answer.

Accepted Answer

$$f^{-1}(x$$) = \frac{6x + 1}{7}$$

Question 10

Simplify $$6\sqrt{3} + 2\sqrt{75}$$ and select the correct answer.

Accepted Answer

$$16\sqrt{3}$$

Question 11

Rationalize the denominator: $$\frac{2}{3 - \sqrt{10}}$$

Accepted Answer

$$-6 - 2\sqrt{10}$$

Question 12

Simplify using properties of exponents: $$(3x^{2/3})(7x$$^{1/4}$$)$

Accepted Answer

$$21x^{11/12}$$

Question 13

A medical researcher uses $$f(x) = (x + 8)^3$ to model a dosage response. What is the inverse function f$$^{-1}$$(x)$$?

Accepted Answer

$$f^{-1}(x$$) = \sqrt[3]{x} - 8$$

Question 14

Let $$f(x) = -5x + 7$$ and $$g(x) = 6x + 4. $$What is $$(f \circ g)(x)$$?

Accepted Answer

$$-30x - 13$$

Question 15

Add or subtract terms if possible: $$-8\sqrt{24} + 7\sqrt{216} - 6\sqrt{54}$$

Accepted Answer

$$8\sqrt{6}$$

Question 16

Find the product $$(9x - 5y)^2$ and select the correct answer.

Accepted Answer

$$81x^2 - 90xy$$ + $$25y^2$$

Question 17

Let $$f(x) = 4x^2$ + 6x + 7$$ and $$g(x) = 6x - 8. $$What is $$(f \circ g)(x)$$?

Accepted Answer

$$144x^2 - 348x + 215$

Question 18

Rationalize the denominator: $$\frac{6}{\sqrt{5} + \sqrt{11}}$$

Accepted Answer

$$\sqrt{11} - \sqrt{5}$$

Question 19

Let $$f(x) = 17x^2$ - 10x$$ and $$g(x) = 9x - 9. $$What is $$(f \circ g)(x)$$?

Accepted Answer

$$1377x^2 - 2844x + 1467$

Question 20

Simplify $$70x^{3/4}$$ / $$10x^{1/3}$$ and select the correct answer.

Accepted Answer

$$7x^{5/12}$$

Precalculus Review: Exponents, Polynomials, Functions, Inverses, and Radicals

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