What is the inverse of f(x)=4(x-1)^2-3 ?

The inverse of f(x)=4(x-1)^2-3 is (sqrt(x+3))/2+1,-(sqrt(x+3))/2+1

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inverse of f(x)=4(x-1)^2-3

inverse

f (x) = 4 (x - 1)^{2} - 3

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

Solution steps

y = 4 (x - 1)^{2} - 3

Replace

x

with

y

x = 4 (y - 1)^{2} - 3

Solve for

y, x = 4 (y - 1)^{2} - 3

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

x + 3 y = 3

y = - 8 x^{3} + 2 x^{5}

y = 5 - x

x^{2} - x

9 e^{- 3 x} x - 6 e^{- 3 x}

What is the inverse of f(x)=4(x-1)^2-3 ?
The inverse of f(x)=4(x-1)^2-3 is (sqrt(x+3))/2+1,-(sqrt(x+3))/2+1