Certainly! Let's solve the given question step by step.
We are given two functions:
- [tex]\( f(x) = 2x + 3 \)[/tex]
- [tex]\( g(x) = x^2 \)[/tex]
We need to find the value of [tex]\( g[f(-3)] \)[/tex].
1. Calculate [tex]\( f(-3) \)[/tex]:
Begin by substituting [tex]\( x = -3 \)[/tex] into the function [tex]\( f(x) \)[/tex]:
[tex]\[
f(-3) = 2(-3) + 3
\][/tex]
2. Simplify the expression:
[tex]\[
f(-3) = -6 + 3 = -3
\][/tex]
3. Calculate [tex]\( g(f(-3)) \)[/tex]:
Now that we have [tex]\( f(-3) = -3 \)[/tex], we need to substitute this result into the function [tex]\( g(x) \)[/tex]:
[tex]\[
g(-3) = (-3)^2
\][/tex]
4. Simplify the expression:
[tex]\[
g(-3) = 9
\][/tex]
Thus, the value of [tex]\( g[f(-3)] \)[/tex] is [tex]\( 9 \)[/tex].
