What is the inverse of f(x)=(x^2+3x-4)/(5x-2) ?

The inverse of f(x)=(x^2+3x-4)/(5x-2) is (-3+5x+sqrt(25x^2-38x+25))/2 ,(-3+5x-sqrt(25x^2-38x+25))/2

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inverse of f(x)=(x^2+3x-4)/(5x-2)

inverse

f (x) = \frac{x ^{2} + 3 x - 4}{5 x - 2}

\frac{- 3 + 5 x + 25 x ^{2} - 38 x + 25}{2}, \frac{- 3 + 5 x - 25 x ^{2} - 38 x + 25}{2}

Solution steps

y = \frac{x ^{2} + 3 x - 4}{5 x - 2}

Replace

x

with

y

x = \frac{y ^{2} + 3 y - 4}{5 y - 2}

Solve for

y, x = \frac{y ^{2} + 3 y - 4}{5 y - 2}

\frac{- 3 + 5 x + 25 x ^{2} - 38 x + 25}{2}, \frac{- 3 + 5 x - 25 x ^{2} - 38 x + 25}{2}

y = x^{2} + x - 5

\frac{2 x + 8}{x - 5}

\frac{2}{3} sin (5 x)

2 - 10

\frac{3}{( s ^{2} + 9 ) ^{2}}

What is the inverse of f(x)=(x^2+3x-4)/(5x-2) ?
The inverse of f(x)=(x^2+3x-4)/(5x-2) is (-3+5x+sqrt(25x^2-38x+25))/2 ,(-3+5x-sqrt(25x^2-38x+25))/2