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1-56.

Consider the functions $f(x)=3x^2-5$ and $g(x)=\sqrt{x-5}+2$. . 1-56 HW eTool (Desmos)  Homework Help ✎

1. What is $f\left(5\right)$?

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

$f(5) = 3(5)^2 - 5$

$f(5) = 75 - 5$

$f(5) = 70$

1. What is $g(5)$?

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

1. What is $f(4)$?

Refer to part (a).

$f(4) = 43$

1. What is $g(4)$?

Refer to part (b).

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

Are there any numbers that can't be squared?

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

1. 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 $5$.

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

See the hints for parts (e) and (f).

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.
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