# What is the inverse function of y=4x^2+3?

Apr 10, 2017

Inverse function is $\frac{\sqrt{x - 3}}{2}$

#### Explanation:

Let $f \left(x\right) = y = 4 {x}^{2} + 3$

Therefore $4 {x}^{2} = y - 3$

and ${x}^{2} = \frac{y - 3}{4}$ i.e. $x = \frac{\sqrt{y - 3}}{2}$

Hence, inverse function of $f \left(x\right) = 4 {x}^{2} + 3$ is ${f}^{- 1} \left(x\right) = \frac{\sqrt{x - 3}}{2}$