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f(x)=4x−k2f(x)= \frac{4x-k}{2} and g(x)=4x−1g(x)=4x-1. If f(g(x))=8xf(g(x))=8x, what is the value of kk?\newlineA) −4-4\newlineB) 00\newlineC) 22\newlineD) 44

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Q. f(x)=4x−k2f(x)= \frac{4x-k}{2} and g(x)=4x−1g(x)=4x-1. If f(g(x))=8xf(g(x))=8x, what is the value of kk?\newlineA) −4-4\newlineB) 00\newlineC) 22\newlineD) 44
  1. Substitute g(x)g(x): Substitute g(x)g(x) into f(x)f(x) to find f(g(x))f(g(x)).\newlinef(g(x))=f(4x−1)=4(4x−1)−k2f(g(x)) = f(4x−1) = \frac{4(4x−1)−k}{2}
  2. Simplify expression: Simplify the expression inside the parentheses. f(g(x))=(16x−4)−k2f(g(x)) = \frac{{(16x-4)-k}}{2}
  3. Multiply out 12\frac{1}{2}: Multiply out the 12\frac{1}{2} to simplify the equation.\newlinef(g(x))=16x−4−k2=8x−2−k2f(g(x)) = \frac{16x−4−k}{2} = 8x−2−\frac{k}{2}

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