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

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

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

inverse

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

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

Solution steps

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

Replace

x

with

y

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

Solve for

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

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

f (x) = x - 4 + 7

(- 4, 1), (8, - 5)

f (x) = 2 - 2 x

2 (4 x^{2} - 5) - 9 + 1

y = x^{2} - 5

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