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

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

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

inverse

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

\frac{x - 3}{2} + 1, - \frac{x - 3}{2} + 1

Solution steps

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

Replace

x

with

y

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

Solve for

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

\frac{x - 3}{2} + 1, - \frac{x - 3}{2} + 1

f (x) = \frac{( 4 + x )}{3 - x}

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

(5, 4), (- 2, 1)

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

f (x) = 2

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