Q: Let $$f(x) = \sqrt{x-2}$$ and $$g(x) = \frac{1}{x-5}. $$What is the domain of $$(f+g)(x)$$?

$$x \u003e 2$$ and $$x \neq 5$$

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

$$x \geq -2$$ \,\text{and}\, x \neq -1$

Question 1

Let $$f(x) = \sqrt{x-2}$$ and $$g(x) = \frac{1}{x-5}. $$What is the domain of $$(f+g)(x)$$?

Accepted Answer

$$x \u003e 2$$ and $$x 
eq 5$$

Question 2

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

Accepted Answer

$$x \geq 0$$

Question 3

Let $$f(x) = \frac{1}{x}$$ and $$g(x) = x^2$ - 4. $$What is the domain of $$(f \circ g)(x)$$?

Accepted Answer

$$x 
eq 2$$ and $$x 
eq -2$$

Question 4

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

Accepted Answer

$$2x^2 + 3$

Question 5

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

Accepted Answer

$$x \geq 4$$

Question 6

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

Accepted Answer

$$x \geq -2$$ \,	ext{and}\, x 
eq -1$

Question 7

Express $$h(x) = 3x^2$ + 7 as a $$composition of two functions $$f$$ and $$g$$ such that $$h(x) = f(g(x)).$$

Accepted Answer

$$f(x) = 3x + 7,\; g(x) = x^2$

Question 8

If $$f(x) = x^2$ and g(x$$) = \frac{1}{x}$$, what is (g$$ \circ f)(x)$$?

Accepted Answer

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

Question 9

A medical dosage is modeled by $$f(x) = \sqrt{x}$$, where $$x is $$the amount of drug administered. If the amount administered is determined by $$g(t) = 4t + 1$$, where $$t is $$time in hours, what is the formula for the effective dosage as a function of time?

Accepted Answer

$$\sqrt{4t + 1}$$

Question 10

Let $$f(x) = \frac{1}{x}$$ and $$g(x) = \sqrt{x-3}. $$What is the domain of $$(f \circ g)(x)$$?

Accepted Answer

$$x \u003e 3$$

Question 11

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

Accepted Answer

$$x 
eq 0$$

Question 12

If $$f(x) = \sqrt{x}$$ and $$g(x) = x^2$ - 9$$, what is the domain of $$(f \circ g)(x)$$?

Accepted Answer

$$x \leq -3 or$$ $$x \geq 3$$

Question 13

A chemical reaction rate is modeled by $$f(x) = \frac{1}{x-2}$$, where $$x is $$the concentration. If the concentration over time is $$g(t) = t^2$ + 2$$, what is the formula for the reaction rate as a function of time?

Accepted Answer

$$\frac{1}{t^2$}$$

Question 14

Let $$f(x) = x^2$ and g(x$$) = \sqrt{x}$$. What is (f$$ \circ g)(x)$$?

Accepted Answer

$$x$$

Question 15

Given $$f(x) = \frac{1}{x}$$ and $$g(x) = \frac{1}{x}$$, what is $$(f \circ g)(x)$$?

Accepted Answer

$$x$$

Question 16

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

Accepted Answer

$$\sqrt{x} + 2$$

Question 17

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

Accepted Answer

$$x \leq -1 or$$ $$x \geq 1$$

Question 18

A population model is $$f(x) = 2x + 1$$, where $$x is $$the number of years since 2000. If the number of years is given by $$g(t) = t^2$, where t$ is the number of decades since 2000, what is the population as a function of t$?

Accepted Answer

$$2t^2 + 1$

Question 19

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

Accepted Answer

$$x \geq 0$$ and $$x 
eq 9$$

Combinations and Compositions of Functions

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