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Mathematics

lolokrat:

f(x)=2x^2+3 and g(x)=x^3 what is g(f(x))? i know the answer is (2x^2+3)^3, but can someone explain the steps?

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Tranquility:

To find g(f(x)), you replace the x in the equation of g(x) with f(x) We know \( g(\color{red}{x})= \color{red}{x}^3\) Then what is \( g(\color{red}{f(x)}) = ??\) Since they tell us f(x) = 2x^2 + 3 You just have to replace the red x with 2x^2 + 3 because that's what f(x) is equal to That's how you get \( g(\color{red}{f(x)}) = \color{red}{(2x^2+3)}^3\)

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