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{:[f(x)=(3x-5)^(3)],[h(x)=2root(3)(x)+8]:} Write h(f(x)) as an expression in terms of x. h(f(x))=

f(x)=(3x−5)3h(x)=2x3+8 \begin{array}{l} f(x)=(3 x-5)^{3} \\ h(x)=2 \sqrt[3]{x}+8 \end{array} \newlineWrite h(f(x)) h(f(x)) as an expression in terms of x x .\newlineh(f(x))= h(f(x))=

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Q. f(x)=(3x−5)3h(x)=2x3+8 \begin{array}{l} f(x)=(3 x-5)^{3} \\ h(x)=2 \sqrt[3]{x}+8 \end{array} \newlineWrite h(f(x)) h(f(x)) as an expression in terms of x x .\newlineh(f(x))= h(f(x))=
  1. Identify functions and question: Identify the functions given and what is being asked.\newlineWe have two functions:\newlinef(x)=(3x−5)3f(x) = (3x - 5)^3\newlineh(x)=2x3+8h(x) = 2\sqrt[3]{x} + 8\newlineWe need to find the composition of the functions, which is h(f(x))h(f(x)).
  2. Substitute f(x)f(x) into h(x)h(x): Substitute f(x)f(x) into h(x)h(x) to find h(f(x))h(f(x)). To find h(f(x))h(f(x)), we replace every instance of xx in h(x)h(x) with f(x)f(x). So, h(f(x))=2(3x−5)33+8h(f(x)) = 2\sqrt[3]{(3x - 5)^3} + 8.
  3. Simplify the expression: Simplify the expression.\newlineSince we have a cube root and a cube, they will cancel each other out.\newlineh(f(x)) = \(2(33x - 55) + 88\.
  4. Distribute and combine like terms: Distribute and combine like terms.\newlineh(f(x))=2×3x−2×5+8h(f(x)) = 2 \times 3x - 2 \times 5 + 8\newlineh(f(x))=6x−10+8h(f(x)) = 6x - 10 + 8\newlineh(f(x))=6x−2.h(f(x)) = 6x - 2.

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