How do you find the inverse of #f(x)= 2x +3#?

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Answer 1 · 2018-03-24T17:09:12

#f^-1(x)=(x-3)/2#

#y=f(x)#

#y=2x+3#

Switch the places of #x# and #y:#

#x=2y+3#

Solve for #y:#

#2y=x-3#

#y=(x-3)/2#

#f^-1(x)=(x-3)/2#

Answer 2 · 2018-03-24T17:10:59

#y=(x-3)/2#

Now, the inverse of a function is just writing #x# in terms of #y#

So #f(x)=2x+3# becomes #y=2x+3#

#y=2x+3# becomes #y-3=2x#

#y-3=2x# becomes #(y-3)/2=x#

or #x=(y-3)/2#

Finally just interchange x and y because we want the function in terms of x.
#y=(x-3)/2#

So #f^-1(x)=(x-3)/2#