Question

Find the inverse function.
x - 3
f(x) =
+ 2
5
f-1(x) = [ ? ]x + [ ]

Answer 1

Answer: 5(x-2) + 3 [aka 5x - 7, whichever form your computer accepts these both mean the same]

Steps
Solve for the inverse function of
f(x)=((x-3)/5)+2

First one should replace the variables so
that f(x)=((x-3)/5)+2 becomes:


x=((y-3)/5)+2 (this isn’t necessary, it just makes it easier for those to remember the variable they are looking for when first learning about inverses) —> regardless, we are searching for y.

So doing regular algebra, we get:

x=((y-3)/5)+2
x-2=((y-3)/5)
5(x-2)=y-3
5(x-2)+3=y

Thus, the inverse: f(x)^-1 = 5x-7