Function Composition - Inputs to Composite Function (Level 2)

Function Composition - Inputs to Composite Function

Level 2

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.

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

$A LaTex expression showing \begin{align*}\text{given:}&\\p(x) &= -3 times x to the power of 2 \\c(x) &= -5x to the power of 2 +1x+4\\p(c(x)) &= ?\end{align*}$

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

A LaTex expression showing p(c(x)) = -3 times (-5x to the power of 2 +1x+4) to the power of 2

A LaTex expression showing p(c(x)) = -5(-3 times x to the power of 2 ) to the power of 2 +1(-3 times x to the power of 2 )+4

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

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

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

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

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

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

A LaTex expression showing m(r(x)) = 3 times (-4square root of -4x) to the power of 2

A LaTex expression showing m(r(x)) = -4square root of -4(3 times x to the power of 2 )

$A LaTex expression showing \begin{align*}\text{given:}&\\z(x) &= 4 over -5x \\n(x) &= -3 over 1x \\z(n(x)) &= ?\end{align*}$

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

a $A LaTex expression showing z(n(x)) = -3 over 1(\frac{4 {-5x})}$

b $A LaTex expression showing z(n(x)) = 4 over -5(\frac{-3 {1x})}$

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

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

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

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

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

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

A LaTex expression showing n(m(x)) = 4 times (3 times x to the power of 2 )+4

A LaTex expression showing n(m(x)) = 3 times (4 times x+4) to the power of 2

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

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

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

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

$A LaTex expression showing \begin{align*}\text{given:}&\\n(x) &= -5x to the power of 2 +1x-4\\p(x) &= -3 over -2x \\n(p(x)) &= ?\end{align*}$

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

A LaTex expression showing n(p(x)) = -5(-3 over -2x ) to the power of 2 +1(-3 over -2x )-4

A LaTex expression showing n(p(x)) = -3 over -2(-5x to the power of 2 +1x-4)