How do you determine whether the function #f(x)=(3x+4)/5# has an inverse and if it does, how do you find the inverse function?

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Answer 1 · 2017-01-13T06:45:55

The inverse function is #f^-1(x)=(5x-4)/3#

Let #y=f(x)=(3x+4)/5#

#5y=3x+4#

#3x=5y-4#

#x=(5y-4)/3#

Then,

#f^-1(x)=(5x-4)/3#

Verification

#f(f^-1(x))=f((5x-4)/3)=((3((5x-4))/3)+4)/5#

#=(5x-4+4)/5=(5x)/5=x#