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

Question

37874 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-09-30T16:36:11

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

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)#

Answer 2 · 2015-09-30T16:42:05

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

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#