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

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

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

inverse

f (x) = \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

f (x) = \frac{7 - 3 x}{2 x - 3}

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

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

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

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

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