Answer
$f^{-1}(x)=\frac{x^{2}-3}{4}$
Work Step by Step
Calculate the inverse of the function $f(x)=\sqrt {4x+3}$
Write $y=f(x)$
$y=\sqrt {4x+3}$
Solve this equation for x in terms of y to get the inverse function.
$x=\frac{y^{2}-3}{4}$
To express $f^{-1}(x)$ as a function of x,interchange x and y. The resulting equation is
$y=\frac{x^{2}-3}{4}$
Therefore, the inverse of the function $f^{-1}(x)=y=\frac{x^{2}-3}{4}$
The graph of the functions $f(x)=\sqrt {4x+3}$ and $f^{-1}(x)=\frac{x^{2}-3}{4}$ along the line $y=x$ on the same screen is depicted below: