What is the inverse of f(x)=2(x-2)^2-1.5 ?

The inverse of f(x)=2(x-2)^2-1.5 is sqrt((x+1.5)/2)+2,-sqrt((x+1.5)/2)+2

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inverse of f(x)=2(x-2)^2-1.5

inverse

f (x) = 2 (x - 2)^{2} - 1.5

\frac{x + 1.5}{2} + 2, - \frac{x + 1.5}{2} + 2

Solution steps

y = 2 (x - 2)^{2} - 1.5

Replace

x

with

y

x = 2 (y - 2)^{2} - 1.5

Solve for

y, x = 2 (y - 2)^{2} - 1.5

\frac{x + 1.5}{2} + 2, - \frac{x + 1.5}{2} + 2

- 4 x^{2} - x - 2

f (x) = x^{2} - 5 x + 3

f (x) = \frac{3 x + 5}{5 x - 4}

f (x) = (2 x)^{- \frac{9}{7}}

f (x) = 2^{- 3}

What is the inverse of f(x)=2(x-2)^2-1.5 ?
The inverse of f(x)=2(x-2)^2-1.5 is sqrt((x+1.5)/2)+2,-sqrt((x+1.5)/2)+2