Plot the graph for the inverse function for f(x) = (1/2)^x

3 Answers

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Karyth Cara | College Teacher | (Level 1) Senior Educator

Posted on

An inverse function is one that undoes another function (in a way similar to reversing algebraic operations where multiplication of numbers can be reversed by division of the same numbers).

To graph an inverse function, use:

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embizze | High School Teacher | (Level 2) Educator Emeritus

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We are asked to plot the graph of the inverse of the function `f(x)=(1/2)^x` :

We can find the inverse: typically you exchange x and y and then solve for y.

`y=(1/2)^x <==> x=(1/2)^y`

Take log base 2 of both sides.

`log_2 x=log_2 (1/2)^y`

`log_2 x=ylog_2 (1/2)`



`y=-log_2 x` is the inverse function


If `y=log_2 x` is the parent function, this function is reflected over the horizontal axis.

(Note that the graph of `f^(-1)(x)=-log_2 x` will be the reflection of the graph of f(x) across the line y=x.)

The graph of the function in black and the inverse in red.

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aruv | High School Teacher | (Level 2) Valedictorian

Posted on


By def. of inverse function

`f^(-1)(f(x))=x`    (i)

Let  f(x)=y



`ln(y)=-x ln(2)`

`x=- ln(y)/ln(2)`        (ii)

Thus from (i) and (ii)


Its graph is