What is the inverse of 1/2 (x-4)^2+1 ?

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

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inverse of 1/2 (x-4)^2+1

inverse

\frac{1}{2} (x - 4)^{2} + 1

2 x - 2 + 4, - 2 x - 2 + 4

Solution steps

y = \frac{1}{2} (x - 4)^{2} + 1

Replace

x

with

y

x = \frac{1}{2} (y - 4)^{2} + 1

Solve for

y, x = \frac{1}{2} (y - 4)^{2} + 1

2 x - 2 + 4, - 2 x - 2 + 4

- 3 (x - 1)^{2} + 2

f (x) = \frac{5 x - 2}{3 x + 1}

f (x) = ln (\frac{e ^{x}}{e ^{x} - 1})

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

f (x) = ln (x^{2} - 4) + π

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