Weaver Hardy
09/07/2023 · Primary School
\( f(x)=(3 x-5)^{3} \) \( h(x)=2 \sqrt[3]{x}+8 \) Write \( h(f(x)) \) as an expression in terms of \( x \) \( h(f(x))=\square \)
UpStudy ThothAI Solution
Tutor-Verified Answer
Step-by-step Solution
To find \( h(f(x)) \), we need to substitute \( f(x) \) into \( h(x) \).
Given:
\[
f(x) = (3x - 5)^3
\]
\[
h(x) = 2 \sqrt[3]{x} + 8
\]
Now, we substitute \( f(x) \) into \( h(x) \):
\[
h(f(x)) = h((3x - 5)^3)
\]
This means we need to evaluate \( h \) at \( (3x - 5)^3 \):
\[
h((3x - 5)^3) = 2 \sqrt[3]{(3x - 5)^3} + 8
\]
The cube root and the cube will cancel each other out:
\[
\sqrt[3]{(3x - 5)^3} = 3x - 5
\]
Thus, we have:
\[
h((3x - 5)^3) = 2(3x - 5) + 8
\]
Now, we simplify this expression:
\[
= 6x - 10 + 8
\]
\[
= 6x - 2
\]
Therefore, the final expression for \( h(f(x)) \) is:
\[
h(f(x)) = 6x - 2
\]
So, we can write:
\[
h(f(x)) = 6x - 2
\]
Quick Answer
\( h(f(x)) = 6x - 2 \)
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