CPM Homework Help : INT3 Problem 7-117

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Home > INT3 > Chapter 7 > Lesson 7.2.5 > Problem 7-117

7-117.

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

What is $f\left(–5\right)$ ?
Hint (a):
Substitute $−5$ for $x$ .

Write an expression for $7g\left(x\right)$ .
Hint (b):
Multiply and distribute $7$ by the $g\left(x\right)$ expression.

What is $f\left(4\right)$ ?
Answer (c):
$43$

Write an expression for $g\left(3x\right)$ .
Answer (d):
$3x − 3$

Write an expression for $f\left(x + 4\right)$ .
Hint (e):
Substitute $x + 4$ for $x$ in the expression.

Write an expression for $g\left(x\right) – f\left(x\right)$ .
Hint (f):
Remember to distribute the negative sign to all terms in $f\left(x\right)$ .
Answer (f):
$−3x^{2} + x + 2$

Describe the domain of $f\left(x\right)$ .
Answer (g):
all real numbers

Describe the domain of $g\left(x\right)$ .
Hint (h):
See part (g).

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