Q: Given $$ h(x) = 6x^3$ - 8x - 7 $$, which of the following best describes the end behavior of $$ h(x) $$?

$$ h(x) \to \infty as$$ $$ x \to \infty $$ and $$ h(x) \to -\infty as$$ $$ x \to -\infty $$

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:

$$ h(g(f(12))) $$

What is the value?

Accepted Answer

$$ 24,553 $$

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 $$ f(x) $$?

Accepted Answer

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

Question 4

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

Accepted Answer

$$ 33 $$

Question 5

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

Accepted Answer

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

Question 6

Given $$ f(x) = x^2$ - 7 $$, for which value of $$ x  is$$ $$ f(x) = 0 $$?

Accepted Answer

$$ x = \sqrt{7} $$ and $$ x = -\sqrt{7} $$

Question 7

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

Accepted Answer

$$ [0, \infty) $$

Question 8

Given $$ h(x) = 6x^3$ - 8x - 7 $$, which of the following best describes the end behavior of $$ h(x) $$?

Accepted Answer

$$ h(x) 	o \infty  as$$ $$ x 	o \infty $$ and $$ h(x) 	o -\infty  as$$ $$ x 	o -\infty $$

Question 9

If $$ f(x) = x^2$ - 7 $$, what is the value of $$ f(g(16)) $$?

Accepted Answer

$$ 9 $$

Question 10

Suppose a scientist models the temperature $$ T  (in $$degrees Celsius) of a chemical reaction as $$ T(x) = 6x^3$ - 8x - 7 $$, where $$ x  is $$the time in hours. What is the temperature after 1 hour?

Accepted Answer

$$ -9 $$

Question 11

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

Accepted Answer

$$ (f \circ g)(x) = x - 7 $$

Question 12

Given $$ h(x) = 6x^3$ - 8x - 7 $$, which of the following is the y-intercept of $$ h(x) $$?

Accepted Answer

$$ -7 $$

Functions and Function Evaluation: College Algebra Review

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