What is the inverse of f(x)= 1/2 (x-1)^2-5 ?

The inverse of f(x)= 1/2 (x-1)^2-5 is sqrt(2x+10)+1,-sqrt(2x+10)+1

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inverse of f(x)= 1/2 (x-1)^2-5

inverse

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

2 x + 10 + 1, - 2 x + 10 + 1

Solution steps

y = \frac{1}{2} (x - 1)^{2} - 5

Replace

x

with

y

x = \frac{1}{2} (y - 1)^{2} - 5

Solve for

y, x = \frac{1}{2} (y - 1)^{2} - 5

2 x + 10 + 1, - 2 x + 10 + 1

(1, 8), (- 2, 5)

(4, 3), (- 1, - 3)

15 x - 5 y = 70

y + 6 = - \frac{1}{2} (x + 8), (- 5, 3)

f (x) = x 4 - x^{2}

What is the inverse of f(x)= 1/2 (x-1)^2-5 ?
The inverse of f(x)= 1/2 (x-1)^2-5 is sqrt(2x+10)+1,-sqrt(2x+10)+1