Question 1

Given the functions $$f(x) = x^2$ - 3x$$ and $$g(x) = 4x - 1$$, what is $$(f \circ g)(x)$$?

Accepted Answer

$$16x^2 - 28x + 7$

Question 2

If $$f(x) = x^2$ - 3x$$ and $$g(x) = 4x - 1$$, what is $$(g \circ f)(x)$$?

Accepted Answer

$$4x^2 - 12x - 1$

Question 3

Evaluate $$(f \circ g)(3)$$ for $$f(x) = x^2$ - 3x$$ and $$g(x) = 4x - 1.$$

Accepted Answer

$$55$$

Question 4

Given $$f(x) = x^2$ - 3x$$ and $$g(x) = 4x - 1$$, what is the domain of $$g \circ f$$?

Accepted Answer

$$(-\infty, \infty)$$

Question 5

If $$k(x) = \dfrac{1}{\sqrt{x^2$-5}}$$, what is the domain of $$k(x)$$?

Accepted Answer

$$x \u003e \sqrt{5} or$$ $$x \u003c -\sqrt{5}$$

Question 6

Given $$h(x) = 2 + (3x + 1)^4$, what is h(-1$$)$$?

Accepted Answer

$$2 + (-2)^4$ = 18$$

Question 7

Suppose $$f(x) = x^2$ - 3x$$ and $$g(x) = 4x - 1. $$Which of the following is equivalent to $$(f \circ g)(x)$$?

Accepted Answer

$$f(g(x))$$

Question 8

If $$f(x) = x^2$ - 3x$$ and $$g(x) = 4x - 1$$, what is $$(g \circ f)(2)$$?

Accepted Answer

$$-13$$

Question 9

Given $$k(x) = \dfrac{1}{\sqrt{x^2$-5}}$$, which of the following $$x$$ values is in the domain of $$k$$?

Accepted Answer

$$x = -4$$

Question 10

If $$h(x) = 2 + (3x + 1)^4$, which of the following best describes the range of h(x$$)$$?

Accepted Answer

$$[2, \infty)$$

Question 11

A biologist models the population of a bacteria culture by $$P(t) = (2t + 1)^2$ - 3(2t + 1)$$, where $$t is $$time in hours. What is the population at $$t = 2$$?

Accepted Answer

$$19$$

Question 12

Given $$f(x) = x^2$ - 3x$$ and $$g(x) = 4x - 1$$, which of the following is the correct expression for $$(f \circ g)(x)$$?

Accepted Answer

$$(4x-1)^2 - 3(4x-1$$)$$

Question 13

If $$f(x) = x^2$ - 3x$$ and $$g(x) = 4x - 1$$, what is $$(f \circ g)(0)$$?

Accepted Answer

$$-4$$

Question 14

Suppose $$k(x) = \dfrac{1}{\sqrt{x^2$-5}}. $$Which of the following statements is true about the domain of $$k(x)$$?

Accepted Answer

$$x^2 - 5$$ \u003e 0$$

Question 15

Given $$h(x) = 2 + (3x + 1)^4$, what is the minimum value of h(x$$)$$?

Accepted Answer

$$2$$

Function Composition and Operations in College Algebra

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