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

The inverse of f(x)=2x^{(2)}-3x-1 is (3+sqrt(8x+17))/4 ,(3-sqrt(8x+17))/4

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

inverse

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

\frac{3 + 8 x + 17}{4}, \frac{3 - 8 x + 17}{4}

Solution steps

y = 2 x^{2} - 3 x - 1

Replace

x

with

y

x = 2 y^{2} - 3 y - 1

Solve for

y, x = 2 y^{2} - 3 y - 1

\frac{3 + 8 x + 17}{4}, \frac{3 - 8 x + 17}{4}

f (x) = \frac{- 6 x + 2}{- 8 x + 9}

f (x) = \frac{9}{- 8 x - 9}

ln (x - 7)

7 x^{2} - 6 x - 1

f (x) = \frac{7 x - 2}{5 x + 1}

What is the inverse of f(x)=2x^{(2)}-3x-1 ?
The inverse of f(x)=2x^{(2)}-3x-1 is (3+sqrt(8x+17))/4 ,(3-sqrt(8x+17))/4