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1-35.

Consider the functions $f(x)=3x^2−5$ and $g(x)=\sqrt{x-5}+2$ . 1-35 HW eTool (Desmos). Homework Help ✎

1. Find $f(5)$ .

Substitute 5 for every x in $f(x)$.

$f(5)=3(5)^2−5$

$f(5)=75−5$

$f(5)=70$

2. Find $g(5)$.

Substitute 5 for every x in $g(x)$.

3. Find f(4).

Refer to part (a).

$f(4)=43$

4. Find g(4).

Refer to part (b).

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5. Find $f(x)+g(x)$.

Add the two equations together.

$(3x^2-5)+(\sqrt{x-5}+2)$

$f(x)+g(x)=3x^2+\sqrt{x-5}-3$

6. Find g(x) − f(x).

Subtract the first equation from the second.

$(\sqrt{x-5}+2)-(3x^2-5)$

$g(x)-f(x)=-3x^2+\sqrt{x-5}+7$

7. Describe the domain of $f(x)$.

Are there any numbers that can't be squared?

The domain of f(x) is all real numbers.

8. Describe the domain of $g(x)$.

What kinds of numbers have no square root? What values of x will keep the expression inside the square root symbol positive or zero?

The domain of $g(x)$ is all numbers greater than or equal to 5.

9. Why is the domain of one of these functions more restrictive than the other?

See to hints for parts (g) and (h).

They are different because the square root of a negative is undefined, whereas
any real number can be squared.

Use the graphed functions in the eTool below to answer each part.
Click the link at right for the full version of the eTool: CCA2 1-35 HW eTool