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

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

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

inverse

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

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

Solution steps

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

Replace

x

with

y

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

Solve for

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

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

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

f (x) = \frac{e ^{x} - 6}{3 - e ^{x}}

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

\frac{2 x + 7}{2}

f (x) = \frac{x}{8 x - 5}

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