Function Inverse - Two Functions to Is Inverse (Exponential/Logarithmic) (Level 1)

Function Inverse - Two Functions to Is Inverse (Exponential/Logarithmic)

Level 1

This topic focuses on determining whether pairs of exponential and logarithmic functions are inverses of each other. It forms part of an introductory tutorial on logarithm functions. The problems typically involve being presented with two mathematical expressions: one exponential and the other logarithmic. The task is to decide whether the second function is the inverse of the first, with 'Yes' or 'No' as the possible answers.

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

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Function Inverse - Two Functions to Is Inverse (Exponential/Logarithmic) Worksheet

Function Inverse - Two Functions to Is Inverse (Exponential/Logarithmic)

$A LaTex expression showing \begin{align*}\text{given:}&\\m(x) &= -2\log{(5 x)}\\y(x) &= 10 to the power of \frac{x over -2 }{5}\end{align*}$

Is y(x) the inverse of m(x)

Yes

$A LaTex expression showing \begin{align*}\text{given:}&\\z(x) &= 4\log{(-3 x)}\\y(x) &= 10 to the power of \frac{x over 4 }{-3}\end{align*}$

Is y(x) the inverse of z(x)

Yes

$A LaTex expression showing \begin{align*}\text{given:}&\\n(x) &= 5 to the power of 2 x \\y(x) &= \frac{\log sub 5 {x}}{2}\end{align*}$

Is y(x) the inverse of n(x)

Yes

$A LaTex expression showing \begin{align*}\text{given:}&\\y(x) &= -4\log sub 2 {(3 x)}\\y(x) &= 2 to the power of \frac{x over -4 }{3}\end{align*}$

Is y(x) the inverse of y(x)

Yes

$A LaTex expression showing \begin{align*}\text{given:}&\\p(x) &= -4 times -3 to the power of 5 x \\y(x) &= \log sub - 3{ \frac{x over -4 }}{5}\end{align*}$

Is y(x) the inverse of p(x)

Yes

$A LaTex expression showing \begin{align*}\text{given:}&\\r(x) &= 2 times -4 to the power of -3 x \\y(x) &= \log sub - 4{ \frac{x over 2 }}{-3}\end{align*}$

Is y(x) the inverse of r(x)

Yes

$A LaTex expression showing \begin{align*}\text{given:}&\\p(x) &= 5\log sub 3 {(-2 x)}\\y(x) &= 3 to the power of \frac{x over 5 }{-2}\end{align*}$

Is y(x) the inverse of p(x)

Yes

$A LaTex expression showing \begin{align*}\text{given:}&\\p(x) &= 5 to the power of 2 x \\y(x) &= \frac{\log sub 5 {x}}{2}\end{align*}$

Is y(x) the inverse of p(x)

Yes