Answer :
To find [tex]\( h(-x) \)[/tex] given the function [tex]\( h(x) = 9x^9 + 4x^3 \)[/tex], you need to substitute [tex]\(-x\)[/tex] for every [tex]\( x \)[/tex] in the expression. Let's break it down step by step:
1. Start with the original expression:
[tex]\[
h(x) = 9x^9 + 4x^3
\][/tex]
2. Substitute [tex]\(-x\)[/tex] for [tex]\(x\)[/tex]:
[tex]\[
h(-x) = 9(-x)^9 + 4(-x)^3
\][/tex]
3. Simplify each term:
- For the first term, [tex]\((-x)^9\)[/tex]:
[tex]\[
(-x)^9 = -x^9 \quad \text{(since the power is odd, the sign is negative)}
\][/tex]
[tex]\[
9(-x)^9 = 9(-x^9) = -9x^9
\][/tex]
- For the second term, [tex]\((-x)^3\)[/tex]:
[tex]\[
(-x)^3 = -x^3 \quad \text{(since the power is odd, the sign is negative)}
\][/tex]
[tex]\[
4(-x)^3 = 4(-x^3) = -4x^3
\][/tex]
4. Combine the simplified terms:
[tex]\[
h(-x) = -9x^9 - 4x^3
\][/tex]
So, the final result is:
[tex]\[
h(-x) = -9x^9 - 4x^3
\][/tex]
1. Start with the original expression:
[tex]\[
h(x) = 9x^9 + 4x^3
\][/tex]
2. Substitute [tex]\(-x\)[/tex] for [tex]\(x\)[/tex]:
[tex]\[
h(-x) = 9(-x)^9 + 4(-x)^3
\][/tex]
3. Simplify each term:
- For the first term, [tex]\((-x)^9\)[/tex]:
[tex]\[
(-x)^9 = -x^9 \quad \text{(since the power is odd, the sign is negative)}
\][/tex]
[tex]\[
9(-x)^9 = 9(-x^9) = -9x^9
\][/tex]
- For the second term, [tex]\((-x)^3\)[/tex]:
[tex]\[
(-x)^3 = -x^3 \quad \text{(since the power is odd, the sign is negative)}
\][/tex]
[tex]\[
4(-x)^3 = 4(-x^3) = -4x^3
\][/tex]
4. Combine the simplified terms:
[tex]\[
h(-x) = -9x^9 - 4x^3
\][/tex]
So, the final result is:
[tex]\[
h(-x) = -9x^9 - 4x^3
\][/tex]
