Question 1

Given the functions:

$$ f(x) = x^2$ - 7 $$

$$ g(x) = \sqrt{x - 7} $$

$$ h(x) = 6x^3$ - 8x - 7 $$

Evaluate the following expression:

$$ h(g(f(2))) $$

What is the value?

Accepted Answer

$$-13$$

Question 2

Which of the following best describes the domain of the function $$g(x) = \sqrt{x - 7}$$?

Accepted Answer

$$x \geq 7$$

Question 3

If $$f(x) = x^2$ - 7$$, what is $$f^{-1}(x$$)$$, the inverse function of f(x$$)$$, for x$$ \geq -7$$?

Accepted Answer

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

Question 4

Suppose $$h(x) = 6x^3$ - 8x - 7. $$What is $$h(2)$$?

Accepted Answer

$$27$$

Question 5

Given $$g(x) = \sqrt{x - 7}$$, for which value of $$x is$$ $$g(x)$$ undefined?

Accepted Answer

$$x = 6$$

Question 6

If $$f(x) = x^2$ - 7$$ and $$g(x) = \sqrt{x - 7}$$, what is $$(g \circ f)(3)$$?

Accepted Answer

$$1$$

Question 7

Which of the following is the correct composition $$(f \circ g)(x)$$ for $$f(x) = x^2$ - 7$$ and $$g(x) = \sqrt{x - 7}$$?

Accepted Answer

$$(f \circ g)(x) = (\sqrt{x - 7})^2$ - 7$$

Question 8

If $$h(x) = 6x^3$ - 8x - 7$$, what is the value of $$h(-1)$$?

Accepted Answer

$$-5$$

Question 9

Given $$f(x) = x^2$ - 7$$, for which value of $$x$$ does $$f(x) = 2$$?

Accepted Answer

$$x = 3$$

Question 10

If $$g(x) = \sqrt{x - 7}$$, what is the range of $$g(x)$$?

Accepted Answer

$$[0, \infty)$$

Functions and Function Evaluation: College Algebra Review

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