Question

Find the inverse of f(x) = -2x+5 The inverse is g(x) = Graph the function and its inverse

Answer 1

Given:

The function is:

$f(x)=-2x+5$

To find:

The inverse of the given function, then draw the graphs of function and its inverse.

Solution:

We have,

$f(x)=-2x+5$

Step 1: Substitute $f(x)=y$ .

$y=-2x+5$

Step 2: Interchange x and y.

$x=-2y+5$

Step 3: Isolate variable y.

$2y=5-x$

$y=\dfrac{5-x}{2}$

Step 4: Substitute $y=f^{-1}(x)$.

$f^{-1}(x)=\dfrac{5-x}{2}$

Therefore, the inverse of the given function is $f^{-1}(x)=\dfrac{5-x}{2}$ and the graphs of these functions are shown below.

Note: The inverse function is $f^{-1}(x)=g(x)$.