Question

what is the inverse of f(x) = (2x - 3)^2? do I take a square root to get rid of the exponent 2?

Answer 1

yes

Answer 2

do I do it to both sides?

Answer 3

you know how to get an inverse, right?

Answer 4

I know an inverse is an opposite, but I'm not good at finding one...

Answer 5

so no

Answer 6

well, you simply firstly, "swap" the variables about, thus \(\bf f(x)={\color{brown}{ y}}=(2{\color{blue}{ x}}-3)^2\qquad \qquad inverse\implies {\color{blue}{ x}}=(2{\color{brown}{ y}}-3)^2\impliedby f^{-1}(x)\)

then solve for "y"

Answer 7

ohhhh okay. so I do the swap, then the square root. I add the 3 next or do I divide by the 2 first?

Answer 8

well, you can divide by 2 if it were a common factor to 2x and 3, but it isn't, so, you'd need to add 3 first


\(\bf f(x)={\color{brown}{ y}}=(2{\color{blue}{ x}}-3)^2\qquad \qquad inverse\implies {\color{blue}{ x}}=(2{\color{brown}{ y}}-3)^2\impliedby f^{-1}(x)
\\ \quad \\
x=(2y-3)^2\implies \sqrt{x}=\sqrt{(2y-3)^2}\implies \sqrt{x}=2y-3
\\ \quad \\
\sqrt{x}+3=2y\implies \cfrac{\sqrt{x}+3}{2}=y\impliedby f^{-1}(x)\)