This math topic focuses on the skill of function composition, specifically calculating the outputs of composite functions. It includes problems that require students to substitute one function into another and simplify the expression to find the result. Each problem is presented with a given pair of functions, and students must calculate the composite function result, choosing from two possible answers. This is part of a broader introduction to function composition and inversion.

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Function Composition - Inputs to Composite Function

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Find the composite function of m(r(x))?

given:m(x)=44xr(x)=3x2m(r(x))=?\begin{align*}\text{given:}&\\m(x) &= -4\sqrt{-4x}\\r(x) &= 3\cdot x^2\\m(r(x)) &= ?\end{align*}

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