Question

find formula for the inverse of the function
f(x)=4x-1/2x+3

Answer 1

\[f(x)= \frac{4x - 1}{2x + 3}\]\[y = \frac{4x - 1}{2x + 3}\]solve for x

Answer 2

so solve for x

Answer 3

multiply both sides by 2x + 3\[y \left( 2x + 3 \right)=4x -1\]\[2xy + 3y = 4x - 1\]\[2xy - 4x = -1 - 3y\]\[x \left( 2y-4 \right)=-1-3y\]\[x = \frac{-1-3y}{2y-4}\]\[f^{-1}(x)=\frac{-1-3x}{2x-4}\]