High School

We appreciate your visit to Given functions tex f x 4x 3 tex and tex g x x 2 2 tex what is the value of tex f g 3. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!

Given functions [tex]f(x) = 4x + 3[/tex] and [tex]g(x) = x^2 - 2[/tex], what is the value of [tex]f(g(-3))[/tex]?

A. -83
B. -41
C. -29
D. 31
E. 79

Answer :

To solve the problem and find the value of [tex]\( f(g(-3)) \)[/tex], we need to first evaluate [tex]\( g(-3) \)[/tex] and then use this result to find [tex]\( f(g(-3)) \)[/tex].

### Step-by-Step Solution

1. Evaluate [tex]\( g(-3) \)[/tex]:

The function [tex]\( g(x) \)[/tex] is given as:
[tex]\[
g(x) = x^2 - 2
\][/tex]

Substitute [tex]\(-3\)[/tex] for [tex]\(x\)[/tex] in the function:
[tex]\[
g(-3) = (-3)^2 - 2
\][/tex]

First, calculate [tex]\((-3)^2\)[/tex]:
[tex]\[
(-3) \times (-3) = 9
\][/tex]

Now, subtract 2 from 9:
[tex]\[
9 - 2 = 7
\][/tex]

Therefore, [tex]\( g(-3) = 7 \)[/tex].

2. Evaluate [tex]\( f(g(-3)) \)[/tex], which is [tex]\( f(7) \)[/tex]:

The function [tex]\( f(x) \)[/tex] is given as:
[tex]\[
f(x) = 4x + 3
\][/tex]

Substitute [tex]\(7\)[/tex] for [tex]\(x\)[/tex] in the function:
[tex]\[
f(7) = 4 \times 7 + 3
\][/tex]

First, multiply 4 by 7:
[tex]\[
4 \times 7 = 28
\][/tex]

Then, add 3:
[tex]\[
28 + 3 = 31
\][/tex]

Therefore, [tex]\( f(7) = 31 \)[/tex].

The value of [tex]\( f(g(-3)) \)[/tex] is [tex]\(\boxed{31}\)[/tex].

Thanks for taking the time to read Given functions tex f x 4x 3 tex and tex g x x 2 2 tex what is the value of tex f g 3. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada