# I want to know how to determine the inverse of a square root functionI want to know how to determine the inverse of a square root function

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For the general function f(x) = sqrt (ax + b), the inverse can be computed as follows.

let y = sqrt (ax + b)

=> y^2 = ax + b

=> ax = y^2 - b

=> x = (y^2 - b)/a

interchange x and y

=> y = (x^2 - b)/a

The inverse of f(x) = sqrt (ax + b) is (x^2 - b)/a

For polynomials of higher order under the square root sign, deriving the inverse would become considerably difficult.

First, we'll noteĀ y= sqrt(ax+b).

Now we'll change x by y:

x= sqrt(ay+b)

We'll raise to square both sides to eliminate the square root:

x^2 = ay + b

We'll isolate y to the left side:

-ay = b - x^2

We'll divide by -a

y = x^2/a - b/a

The inverse function is:

f^-1(x) = x^2/a - b/a