Function Composition - Inputs to Composite Function (Level 1)

Function Composition - Inputs to Composite Function

Level 1

This math topic focuses on the skill of function composition, specifically determining the output of a composite function for given component functions. It involves substituting one function into another and evaluating the result. Multiple choice questions provide expressions of composed functions, requiring the correct formulation of these composite functions from the algebraic expressions given. This topic aligns with introductory concepts in the unit of functions, addressing the broader subjects of composition and inversion of functions.

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

$A LaTex expression showing \begin{align*}\text{given:}&\\r(x) &= 1 times x-5\\d(x) &= 5 over 2x \\r(d(x)) &= ?\end{align*}$

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

A LaTex expression showing r(d(x)) = 1 times (5 over 2x )-5

A LaTex expression showing r(d(x)) = 5 over 2(1 times x-5)

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

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

A LaTex expression showing b(y(x)) = -4 times (-1 over 4x )-3

A LaTex expression showing b(y(x)) = -1 over 4(-4 times x-3)

$A LaTex expression showing \begin{align*}\text{given:}&\\d(x) &= 4 times x-1\\c(x) &= 2 times x-2\\d(c(x)) &= ?\end{align*}$

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

A LaTex expression showing d(c(x)) = 4 times (2 times x-2)-1

A LaTex expression showing d(c(x)) = 2 times (4 times x-1)-2

$A LaTex expression showing \begin{align*}\text{given:}&\\y(x) &= -2 over -5x \\p(x) &= -1 times x+3\\y(p(x)) &= ?\end{align*}$

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

A LaTex expression showing y(p(x)) = -1 times (-2 over -5x )+3

A LaTex expression showing y(p(x)) = -2 over -5(-1 times x+3)

$A LaTex expression showing \begin{align*}\text{given:}&\\d(x) &= 4 over -5x \\z(x) &= 5 times x+2\\d(z(x)) &= ?\end{align*}$

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

A LaTex expression showing d(z(x)) = 4 over -5(5 times x+2)

A LaTex expression showing d(z(x)) = 5 times (4 over -5x )+2

$A LaTex expression showing \begin{align*}\text{given:}&\\r(x) &= 5 times x-4\\b(x) &= 3 times x-3\\r(b(x)) &= ?\end{align*}$

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

A LaTex expression showing r(b(x)) = 5 times (3 times x-3)-4

A LaTex expression showing r(b(x)) = 3 times (5 times x-4)-3

$A LaTex expression showing \begin{align*}\text{given:}&\\b(x) &= -1 times x+3\\p(x) &= 3 over 1x \\b(p(x)) &= ?\end{align*}$

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

A LaTex expression showing b(p(x)) = -1 times (3 over 1x )+3

A LaTex expression showing b(p(x)) = 3 over 1(-1 times x+3)

$A LaTex expression showing \begin{align*}\text{given:}&\\n(x) &= 3 over 3x \\b(x) &= -1 over -2x \\n(b(x)) &= ?\end{align*}$

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

a $A LaTex expression showing n(b(x)) = -1 over -2(\frac{3 {3x})}$

b $A LaTex expression showing n(b(x)) = 3 over 3(\frac{-1 {-2x})}$