Function Composition - Inputs to Composite Function (Level 3)

Function Composition - Inputs to Composite Function

Level 3

This math topic focuses on function composition, specifically finding the output of composite functions like c(r(x)), r(p(x)), b(r(x)), y(m(x)), b(m(x)), p(n(x)), and n(d(x)). Each of these problems involves substituting one function into another and simplifying the resulting expression to evaluate the composite function at given inputs. The skill practiced here helps deepen understanding of function operations and their interactions, which is fundamental in algebra and precalculus studies.

Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

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Function Composition - Inputs to Composite Function Worksheet

Function Composition - Inputs to Composite Function

$A LaTex expression showing \begin{align*}\text{given:}&\\y(x) &= 1square root of -1x\\p(x) &= 3x to the power of 2 -5x+2\\p(y(x)) &= ?\end{align*}$

Find the composite function of p(y(x))?

A LaTex expression showing p(y(x)) = 3(1square root of -1x) to the power of 2 -5(1square root of -1x)+2

A LaTex expression showing p(y(x)) = 1square root of -1(3x to the power of 2 -5x+2)

$A LaTex expression showing \begin{align*}\text{given:}&\\y(x) &= 5\log{-3x}\\n(x) &= -5 to the power of 1x \\n(y(x)) &= ?\end{align*}$

Find the composite function of n(y(x))?

a $A LaTex expression showing n(y(x)) = 5\log{-3(-5 to the power of 1x )}$

b $A LaTex expression showing n(y(x)) = -5 to the power of 1(5\log{-3x )}$

$A LaTex expression showing \begin{align*}\text{given:}&\\p(x) &= -1square root of -2x\\b(x) &= 5x to the power of 3 -5x to the power of 2 -2x\\p(b(x)) &= ?\end{align*}$

Find the composite function of p(b(x))?

A LaTex expression showing p(b(x)) = 5(-1square root of -2x) to the power of 3 -5(-1square root of -2x) to the power of 2 -2(-1square root of -2x)

A LaTex expression showing p(b(x)) = -1square root of -2(5x to the power of 3 -5x to the power of 2 -2x)

$A LaTex expression showing \begin{align*}\text{given:}&\\p(x) &= -3 times x to the power of 2 \\r(x) &= 1x to the power of 2 -2x+4\\r(p(x)) &= ?\end{align*}$

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

A LaTex expression showing r(p(x)) = 1(-3 times x to the power of 2 ) to the power of 2 -2(-3 times x to the power of 2 )+4

A LaTex expression showing r(p(x)) = -3 times (1x to the power of 2 -2x+4) to the power of 2

$A LaTex expression showing \begin{align*}\text{given:}&\\p(x) &= 1 times x to the power of 2 \\d(x) &= 2 to the power of -5x \\p(d(x)) &= ?\end{align*}$

Find the composite function of p(d(x))?

A LaTex expression showing p(d(x)) = 2 to the power of -5(1 times x^2)

A LaTex expression showing p(d(x)) = 1 times (2 to the power of -5x ) to the power of 2

$A LaTex expression showing \begin{align*}\text{given:}&\\z(x) &= 2 to the power of -3x \\m(x) &= -5square root of -2x\\m(z(x)) &= ?\end{align*}$

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

A LaTex expression showing m(z(x)) = 2 to the power of -3(-5square root of -2x)

A LaTex expression showing m(z(x)) = -5square root of -2(2 to the power of -3x)

$A LaTex expression showing \begin{align*}\text{given:}&\\p(x) &= -3square root of -5x\\y(x) &= 3x to the power of 2 -2x-1\\p(y(x)) &= ?\end{align*}$

Find the composite function of p(y(x))?

A LaTex expression showing p(y(x)) = 3(-3square root of -5x) to the power of 2 -2(-3square root of -5x)-1

A LaTex expression showing p(y(x)) = -3square root of -5(3x to the power of 2 -2x-1)

$A LaTex expression showing \begin{align*}\text{given:}&\\m(x) &= -1 times x to the power of 2 \\y(x) &= -2 to the power of 2x \\y(m(x)) &= ?\end{align*}$

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

A LaTex expression showing y(m(x)) = -1 times (-2 to the power of 2x ) to the power of 2

A LaTex expression showing y(m(x)) = -2 to the power of 2(-1 times x^2)