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

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

inverse

f (x) = 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

4 x^{2} - 28 x + 16 y - 31 = 0

3 + x

- x^{2} - 1

f (x) = 7 + 5 x - 5

f (x) = 30 n + 400

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