Question

How do you solve f^-1(3)= when f(x)=2x-7 /3?

Answer 1

First you need to find the inverse of \(f(x)\).

Answer 2

\(f(x) = \Large\frac{2x-7}{3}\) or \(f(x) = 2x-\Large\frac{7}{3}\) ?

Answer 3

The first one

Answer 4

Ok. Take \(f(x)\) as \(y=\Large\frac{2x-7}{3}\) . Now swap \(x\) and \(y\) and solve for \(y \) again. Give a try.

Answer 5

y=2x-7/3
x=2y-7/3
3x=2y-7
3x+7=2y
3x+7/2=y
Is this right?

Answer 6

Correct. Now \(f^{-1}(x) = \large\frac{3x+7}{2}\). Substitute 3 for \(x\) and solve. :)

Answer 7

f^-1(x)=3x+7/2
f^-1(3)=3(3)+7/2
f^-1(3)=16/2
f^-1(3)= 8
Is this right?

Answer 8

That's right!

Answer 9

Thank you:)