Question

Find f^-1(x) given that f (x) is 2/3-4x

Answer 1

f(x) = 2 x 1/3-4x
let's break it down:
1. multiply 4 by x
2. subtract product from 3
3. divide 1 by the resut of step 2
4 and multiply resut of step 3 by 2
Now let's do the opposite:
1. divide 4 by x = 4/x
2. add product to 3= 3+4/x
3. multiply 1 by result = 3+4/x
4 divide resut of step 3 by 2 = 3+4x/2

Check: let x = 2
f(x) = 2/3 + 4(2) = 2/11
F^-1(x) = 3+4(2)/2 = 11/2

Answer 2

\[
y=2/3-4x\\
4 x = 2/3 -y\\
x= 1/6 -y/4\\

f^{-1}(x)=1/6 -x/4

\]