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

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

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

inverse

f (x) = (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}

f (x) = \frac{7}{x ^{2} + 1}

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

f (x) = \frac{2 x - 6}{- x + 4}

f (x) = x^{2} + y = 36

f (x) = 3 - 5 x

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