What is the inverse of g(x)=sqrt(12-2x)+5/2 ?

The inverse of g(x)=sqrt(12-2x)+5/2 is -(4x^2-20x-23)/8

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inverse of g(x)=sqrt(12-2x)+5/2

inverse

g (x) = 12 - 2 x + \frac{5}{2}

- \frac{4 x ^{2} - 20 x - 23}{8}

Solution steps

y = 12 - 2 x + \frac{5}{2}

Replace

x

with

y

x = 12 - 2 y + \frac{5}{2}

Solve for

y, x = 12 - 2 y + \frac{5}{2}

- \frac{4 x ^{2} - 20 x - 23}{8}

(3 x - \frac{1}{5}) (3 x + \frac{1}{5})

y = 0.4 x - 19

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

f (x) = \frac{6 x + 2}{5 x - 7}

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

What is the inverse of g(x)=sqrt(12-2x)+5/2 ?
The inverse of g(x)=sqrt(12-2x)+5/2 is -(4x^2-20x-23)/8