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f(x)=x^(3)-6 h(x)=root(3)(2x-15) Write f(h(x)) as an expression in terms of x. f(h(x))=

f(x)=x3−6 f(x)=x^{3}-6 \newlineh(x)=2x−153 h(x)=\sqrt[3]{2 x-15} \newlineWrite f(h(x)) f(h(x)) as an expression in terms of x x .\newlinef(h(x))= f(h(x))=

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Q. f(x)=x3−6 f(x)=x^{3}-6 \newlineh(x)=2x−153 h(x)=\sqrt[3]{2 x-15} \newlineWrite f(h(x)) f(h(x)) as an expression in terms of x x .\newlinef(h(x))= f(h(x))=
  1. Identify functions and question: First, we need to identify the functions given and what is being asked. We have two functions:\newlinef(x)=x3−6f(x) = x^3 - 6\newlineh(x)=2x−153h(x) = \sqrt[3]{2x - 15}\newlineWe are asked to find the composition of these functions, which is f(h(x))f(h(x)).
  2. Substitute h(x)h(x) into f(x)f(x): To find f(h(x))f(h(x)), we need to substitute the expression for h(x)h(x) into the function f(x)f(x) wherever there is an xx. So, we will replace xx in f(x)f(x) with 2x−153\sqrt[3]{2x - 15}.
  3. Perform the substitution: Now, we perform the substitution: f(h(x))=(2x−153)3−6f(h(x)) = (\sqrt[3]{2x - 15})^3 - 6
  4. Simplify the expression: Next, we simplify the expression. When we raise a cube root to the power of 33, they cancel each other out, so we are left with:\newlinef(h(x))=(2x−15)−6f(h(x)) = (2x - 15) - 6
  5. Combine like terms: Finally, we simplify the expression by combining like terms:\newlinef(h(x))=2x−15−6f(h(x)) = 2x - 15 - 6\newlinef(h(x))=2x−21f(h(x)) = 2x - 21

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