$$x \u003e 0$$ and $$\sqrt{x} \neq 2$$

Question 1

Which of the following values must be excluded from the domain of the function $$f(x) = \frac{1}{x-3}$$?

Accepted Answer

$$x = 3$$

Question 2

Given $$f(x) = \sqrt{x-2}$$, what is the domain of $$f$$?

Accepted Answer

$$[2, \infty)$$

Question 3

If $$f(x) = x^2$ and g(x) = x+1$, what is (f+g)(x$$)$$?

Accepted Answer

$$x^2 + x + 1$

Question 4

Let $$f(x) = \frac{1}{x}$$ and $$g(x) = \sqrt{x}. $$What is the domain of $$(f \cdot g)(x)$$?

Accepted Answer

$$x \u003e 0$$

Question 5

Given $$f(x) = x^2$ and g(x) = 2x+1$, what is (f$$ \circ g)(x)$$?

Accepted Answer

$$(2x+1)^2$$

Question 6

If $$f(x) = \sqrt{x}$$ and $$g(x) = x-4$$, what is the domain of $$(f \circ g)(x)$$?

Accepted Answer

$$x \geq 4$$

Question 7

Which of the following is the correct expression for $$(f/g)(x) if$$ $$f(x) = x^2$ - 1$$ and $$g(x) = x+1$$?

Accepted Answer

$$\frac{x^2$-1}{x+1}$$

Question 8

Suppose $$f(x) = \frac{1}{x-2}$$ and $$g(x) = \sqrt{x}. $$What is the domain of $$(f \circ g)(x)$$?

Accepted Answer

$$x \u003e 0$$ and $$\sqrt{x} 
eq 2$$

Question 9

If $$h(x) = (3x+1)^2$, which of the following expresses h$ as a composition of two functions f$ and g$?

Accepted Answer

$$f(x) = x^2$, \ g(x) = 3x+1$

Question 10

A chemist models the concentration of a substance as $$C(t) = \frac{1}{\sqrt{t-1}}. $$For what values of $$t is $$this model valid?

Accepted Answer

$$t \u003e 1$$

Question 11

Given $$f(x) = x^2$ and g(x$$) = \frac{1}{x}$$, what is the domain of (f+g)(x$$)$$?

Accepted Answer

$$x 
eq 0$$

Question 12

If $$f(x) = \sqrt{x+3}$$ and $$g(x) = x-1$$, what is the domain of $$(f \circ g)(x)$$?

Accepted Answer

$$x \geq -2$$

Question 13

A medical researcher uses $$f(x) = \frac{1}{x-5} to $$model a dosage. What value of $$x$$ must be excluded from the domain?

Accepted Answer

$$x = 5$$

Question 14

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

Accepted Answer

$$x \geq 0$$

Question 15

Given $$f(x) = \sqrt{5-x}$$ and $$g(x) = x^2$, what is the domain of (f$$ \circ g)(x)$$?

Accepted Answer

$$x^2$$ \leq 5$$

Combinations and Compositions of Functions: Domains and Operations

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