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

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

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

inverse

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

x + 3 + 1, - x + 3 + 1

Solution steps

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

Replace

x

with

y

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

Solve for

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

x + 3 + 1, - x + 3 + 1

(y + 2) = \frac{1}{3} (x + 9)

f (x) = \frac{5 x}{4}

6 x^{3} + \frac{9}{x}

f (x) = ln (5 - 2 x)

f (x) = \frac{3 x - 4}{x + 2}

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