Answer :
Sure, let's find [tex]\( h(-x) \)[/tex] for the given function [tex]\( h(x) = 3x^9 - 9x^7 \)[/tex].
To do this, we substitute [tex]\(-x\)[/tex] for [tex]\(x\)[/tex] in the function [tex]\( h(x) \)[/tex]:
1. Start with the given function:
[tex]\[
h(x) = 3x^9 - 9x^7
\][/tex]
2. Substitute [tex]\(-x\)[/tex] into the function in place of [tex]\(x\)[/tex]:
[tex]\[
h(-x) = 3(-x)^9 - 9(-x)^7
\][/tex]
3. Now, calculate the powers of [tex]\(-x\)[/tex]:
- [tex]\((-x)^9 = -x^9\)[/tex] because raising [tex]\(-x\)[/tex] to an odd power results in a negative value.
- [tex]\((-x)^7 = -x^7\)[/tex] for the same reason (odd power).
4. Substitute these values back into the expression:
[tex]\[
h(-x) = 3(-x^9) - 9(-x^7)
\][/tex]
5. Simplify the expression:
[tex]\[
h(-x) = -3x^9 + 9x^7
\][/tex]
So, the function [tex]\( h(-x) \)[/tex] is:
[tex]\[
h(-x) = -3x^9 + 9x^7
\][/tex]
This is the detailed step-by-step solution to finding [tex]\( h(-x) \)[/tex].
To do this, we substitute [tex]\(-x\)[/tex] for [tex]\(x\)[/tex] in the function [tex]\( h(x) \)[/tex]:
1. Start with the given function:
[tex]\[
h(x) = 3x^9 - 9x^7
\][/tex]
2. Substitute [tex]\(-x\)[/tex] into the function in place of [tex]\(x\)[/tex]:
[tex]\[
h(-x) = 3(-x)^9 - 9(-x)^7
\][/tex]
3. Now, calculate the powers of [tex]\(-x\)[/tex]:
- [tex]\((-x)^9 = -x^9\)[/tex] because raising [tex]\(-x\)[/tex] to an odd power results in a negative value.
- [tex]\((-x)^7 = -x^7\)[/tex] for the same reason (odd power).
4. Substitute these values back into the expression:
[tex]\[
h(-x) = 3(-x^9) - 9(-x^7)
\][/tex]
5. Simplify the expression:
[tex]\[
h(-x) = -3x^9 + 9x^7
\][/tex]
So, the function [tex]\( h(-x) \)[/tex] is:
[tex]\[
h(-x) = -3x^9 + 9x^7
\][/tex]
This is the detailed step-by-step solution to finding [tex]\( h(-x) \)[/tex].
