What is the inverse of f(x)= 1/2 x^2-4x+39/8 ?

The inverse of f(x)= 1/2 x^2-4x+39/8 is (8+sqrt(8x+25))/2 ,(8-sqrt(8x+25))/2

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inverse of f(x)= 1/2 x^2-4x+39/8

inverse

f (x) = \frac{1}{2} x^{2} - 4 x + \frac{39}{8}

\frac{8 + 8 x + 25}{2}, \frac{8 - 8 x + 25}{2}

Solution steps

y = \frac{1}{2} x^{2} - 4 x + \frac{39}{8}

Replace

x

with

y

x = \frac{1}{2} y^{2} - 4 y + \frac{39}{8}

Solve for

y, x = \frac{1}{2} y^{2} - 4 y + \frac{39}{8}

\frac{8 + 8 x + 25}{2}, \frac{8 - 8 x + 25}{2}

\frac{x ^{2} + x - 30}{x - 6}

f (x) = - (x + 1) 2 - 1, x < - \frac{π}{2}

\frac{6 x}{x - 4}

f (x) = \frac{( 2 x + 5 )}{( x - 11 )}

\frac{( x - 1 ) ^{7} + 5}{3}

What is the inverse of f(x)= 1/2 x^2-4x+39/8 ?
The inverse of f(x)= 1/2 x^2-4x+39/8 is (8+sqrt(8x+25))/2 ,(8-sqrt(8x+25))/2