What is the inverse function of f(x) =2x-5?

2 Answers
Sep 30, 2015

y =f^-1 (x)= 1/2 (x+5)

Explanation:

Write y= 2x-5 and now interchange x and y.

It becomes x= 2y-5.

Now solve for y =f^-1 (x)= 1/2 (x+5)

Sep 30, 2015

g(x)=(x+5)/2
is the inverse function of f(x)=2x-5

Explanation:

Define g(x) as the inverse function of f(x)=2x-5

By definition of inverse function:
color(green)(f(g(x))) = color(red)(x)

Since f(x)=2x-5
rArr color(green)(f(g(x))) = color(blue)(2g(x)-5)

rArr color(blue)(2g(x)-5) = color(red)(x)

rArr2g(x) = x+5

rArrg(x) = (x+5)/2