To solve for [tex]\( f(g(2)) \)[/tex], we need to follow a systematic series of steps:
1. Understand the Functions:
- We are given two functions: [tex]\( f(x) = 5x + 2 \)[/tex] and [tex]\( g(x) = x^3 - 4 \)[/tex].
2. Calculate [tex]\( g(2) \)[/tex]:
- First, substitute [tex]\( x \)[/tex] with 2 in the function [tex]\( g(x) \)[/tex].
- So, [tex]\( g(2) \)[/tex] means replacing [tex]\( x \)[/tex] with 2 in [tex]\( g(x) = x^3 - 4 \)[/tex].
[tex]\[
g(2) = 2^3 - 4
\][/tex]
- Calculating [tex]\( 2^3 \)[/tex]:
[tex]\[
2^3 = 8
\][/tex]
- Subtract 4 from 8:
[tex]\[
8 - 4 = 4
\][/tex]
- Therefore, [tex]\( g(2) = 4 \)[/tex].
3. Calculate [tex]\( f(g(2)) \)[/tex]:
- Now that we know [tex]\( g(2) = 4 \)[/tex], we need to find [tex]\( f(4) \)[/tex].
- Substitute [tex]\( x \)[/tex] with 4 in the function [tex]\( f(x) = 5x + 2 \)[/tex].
[tex]\[
f(4) = 5(4) + 2
\][/tex]
- Multiplying 5 by 4:
[tex]\[
5 \times 4 = 20
\][/tex]
- Add 2 to the product:
[tex]\[
20 + 2 = 22
\][/tex]
- Therefore, [tex]\( f(4) = 22 \)[/tex].
Hence, the answer to [tex]\( f(g(2)) \)[/tex] is:
[tex]\[
f(g(2)) = f(4) = 22
\][/tex]
