Question

Lets find F^(-1) if
y=-2x+1
I’m not sure if the F^(-1)=1+x/2

Answer 1

So, again, we have our rules for mapping
`y` to
`x`:


`y=-2x+1`

To find
`f^(-1)`, we solve for
`x`.


`y-1=(-2x+1)-1` (subtract 1 from both sides)

`(y-1)/(-2)=(-2x)/(-2)` (divide both sides by -2)

That gives us


`x= (y-1)/(-2)`

Now that we have a way of mapping
`y` back to
`x`, all we do is swap the domain and range, and we have


`f^(-1)(x)= (x-1)/(-2)`

Answer 2

close enough, let's do the switcharoo of the variables and solve for "y".


`\bf y=-2x+1\qquad \boxed{x}=-2\boxed{y}+1\implies x-1=-2y \\\\\\ \cfrac{x-1}{-2}=y\implies \cfrac{1-x}{2}=\stackrel{f^(-1)}{y}`