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

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

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

inverse

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

2 x - 2 + 3, - 2 x - 2 + 3

Solution steps

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

Replace

x

with

y

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

Solve for

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

2 x - 2 + 3, - 2 x - 2 + 3

- x^{2} + 16

2 x^{3} - 8

f (x) = (3^{x} + 2)^{2} + 4

f (x) = (5 x^{3} - 1) + 7

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