### Home > INT3 > Chapter 7 > Lesson 7.2.5 > Problem7-117

7-117.

Use the functions $f\left(x\right) = 3x^{2} – 5$ and $g\left(x\right) = x – 3$ to complete the parts below.

1. What is $f\left(–5\right)$?

Substitute $−5$ for $x$.

1. Write an expression for $7g\left(x\right)$.

Multiply and distribute $7$ by the $g\left(x\right)$ expression.

1. What is $f\left(4\right)$?

$43$

1. Write an expression for $g\left(3x\right)$.

$3x − 3$

1. Write an expression for $f\left(x + 4\right)$.

Substitute $x + 4$ for $x$ in the expression.

1. Write an expression for $g\left(x\right) – f\left(x\right)$.

Remember to distribute the negative sign to all terms in $f\left(x\right)$.

$−3x^{2} + x + 2$

1. Describe the domain of $f\left(x\right)$.

all real numbers

1. Describe the domain of $g\left(x\right)$.

See part (g).