Question

Pls help!!!!!!
how do we find the inverse of below function in terms of f inverse
r(x)=1-2f(3-4x)

Answer 1

we can do this

Answer 2

start as usual by writing
\[y=1-2f(3-4x)\] then switch x and y to get
\[x=1-2f(3-4y)\] and solve for \(y\)

Answer 3

subtract 1

\[x-1=-2f(3-4y)\]
divide by -2
\[\frac{1-x}{2}=f(3-4y)\]

Answer 4

now comes the \(f^{-1}\) part since we want to solve for what is inside the function
\[f^{-1}(\frac{1-x}{2})=3-4y\]
subtract 3
\[f^{-1}(\frac{1-x}{2})-3=-4y\] divide by -4
\[\frac{3-f^{-1}(\frac{1-x}{2})}{4}=y\] and we are done

Answer 5

thank you

Answer 6

yw