What is the inverse of (2x-3)^2-1 ?

The inverse of (2x-3)^2-1 is (sqrt(x+1)+3)/2 ,(-sqrt(x+1)+3)/2

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inverse of (2x-3)^2-1

inverse

(2 x - 3)^{2} - 1

\frac{x + 1 + 3}{2}, \frac{- x + 1 + 3}{2}

Solution steps

y = (2 x - 3)^{2} - 1

Replace

x

with

y

x = (2 y - 3)^{2} - 1

Solve for

y, x = (2 y - 3)^{2} - 1

\frac{x + 1 + 3}{2}, \frac{- x + 1 + 3}{2}

6 x^{3} - 9 x^{2} - 36 x

f (x) = \frac{1}{4} x - 9

f (x) = 16 - 4 x

3 x (x - 2)^{3}

f (x) = \frac{x}{x + 4}

What is the inverse of (2x-3)^2-1 ?
The inverse of (2x-3)^2-1 is (sqrt(x+1)+3)/2 ,(-sqrt(x+1)+3)/2