What is the inverse of f(x)=sqrt(12-2x)-3/2 ?

The inverse of f(x)=sqrt(12-2x)-3/2 is -(4x^2+12x-39)/8

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inverse of f(x)=sqrt(12-2x)-3/2

inverse

f (x) = 12 - 2 x - \frac{3}{2}

- \frac{4 x ^{2} + 12 x - 39}{8}

Solution steps

y = 12 - 2 x - \frac{3}{2}

Replace

x

with

y

x = 12 - 2 y - \frac{3}{2}

Solve for

y, x = 12 - 2 y - \frac{3}{2}

- \frac{4 x ^{2} + 12 x - 39}{8}

What is the inverse of f(x)=sqrt(12-2x)-3/2 ?
The inverse of f(x)=sqrt(12-2x)-3/2 is -(4x^2+12x-39)/8