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

The inverse of f(x)= 1/2 (x-1)^2+3 is sqrt(2x-6)+1,-sqrt(2x-6)+1

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

inverse

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

2 x - 6 + 1, - 2 x - 6 + 1

Solution steps

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

Replace

x

with

y

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

Solve for

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

2 x - 6 + 1, - 2 x - 6 + 1

What is the inverse of f(x)= 1/2 (x-1)^2+3 ?
The inverse of f(x)= 1/2 (x-1)^2+3 is sqrt(2x-6)+1,-sqrt(2x-6)+1