Answer :
Sure! Let's work through finding [tex]\((f^{\circ} g)(x)\)[/tex] step by step. The notation [tex]\(f^{\circ} g\)[/tex] represents the composition of the functions [tex]\(f(x)\)[/tex] and [tex]\(g(x)\)[/tex], which means you substitute [tex]\(g(x)\)[/tex] into [tex]\(f(x)\)[/tex].
Given:
- [tex]\(f(x) = -4x + 7\)[/tex]
- [tex]\(g(x) = x^3\)[/tex]
We need to find [tex]\(f(g(x))\)[/tex], which means we will input [tex]\(g(x)\)[/tex] into [tex]\(f(x)\)[/tex]:
1. Start with the expression for [tex]\(g(x)\)[/tex]:
[tex]\[
g(x) = x^3
\][/tex]
2. Substitute [tex]\(g(x)\)[/tex] into [tex]\(f(x)\)[/tex]:
[tex]\[
f(g(x)) = f(x^3)
\][/tex]
3. Replace every [tex]\(x\)[/tex] in [tex]\(f(x) = -4x + 7\)[/tex] with [tex]\(x^3\)[/tex]:
[tex]\[
f(x^3) = -4(x^3) + 7
\][/tex]
Thus, the expression for [tex]\((f^{\circ} g)(x)\)[/tex] is:
[tex]\[
-4x^3 + 7
\][/tex]
So, the correct choice is:
[tex]\[
-4x^3 + 7
\][/tex]
Given:
- [tex]\(f(x) = -4x + 7\)[/tex]
- [tex]\(g(x) = x^3\)[/tex]
We need to find [tex]\(f(g(x))\)[/tex], which means we will input [tex]\(g(x)\)[/tex] into [tex]\(f(x)\)[/tex]:
1. Start with the expression for [tex]\(g(x)\)[/tex]:
[tex]\[
g(x) = x^3
\][/tex]
2. Substitute [tex]\(g(x)\)[/tex] into [tex]\(f(x)\)[/tex]:
[tex]\[
f(g(x)) = f(x^3)
\][/tex]
3. Replace every [tex]\(x\)[/tex] in [tex]\(f(x) = -4x + 7\)[/tex] with [tex]\(x^3\)[/tex]:
[tex]\[
f(x^3) = -4(x^3) + 7
\][/tex]
Thus, the expression for [tex]\((f^{\circ} g)(x)\)[/tex] is:
[tex]\[
-4x^3 + 7
\][/tex]
So, the correct choice is:
[tex]\[
-4x^3 + 7
\][/tex]
