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

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Answer 1 · 2018-05-28T07:07:28

Consider #y=-5x+2#

Our goal is to find the anti-image of x

#y-2=-5x#

#x=(-y+2)/5#

Then the function inverse is #y=(-x+2)/5=f^(-1)(x)#

We can test the solution solving #f o f^(-1)#

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

So #fof^(-1)=identity# and #f^(-1)# is the inverse of #f#