What is the inverse of f(x)=(5x^2-6)/(3x+8) ?

The inverse of f(x)=(5x^2-6)/(3x+8) is (3x+sqrt(9x^2-20(-6-8x)))/(10),(3x-sqrt(9x^2-20(-6-8x)))/(10)

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inverse of f(x)=(5x^2-6)/(3x+8)

inverse

f (x) = \frac{5 x ^{2} - 6}{3 x + 8}

\frac{3 x + 9 x ^{2} - 20 ( - 6 - 8 x )}{10}, \frac{3 x - 9 x ^{2} - 20 ( - 6 - 8 x )}{10}

Solution steps

y = \frac{5 x ^{2} - 6}{3 x + 8}

Replace

x

with

y

x = \frac{5 y ^{2} - 6}{3 y + 8}

Solve for

y, x = \frac{5 y ^{2} - 6}{3 y + 8}

\frac{3 x + 9 x ^{2} - 20 ( - 6 - 8 x )}{10}, \frac{3 x - 9 x ^{2} - 20 ( - 6 - 8 x )}{10}

f (x) = \frac{6}{2 x - 1}

f (x) = 2 x^{2} - 9

y = 2 x - 5

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

f (x) = 2 + x

What is the inverse of f(x)=(5x^2-6)/(3x+8) ?
The inverse of f(x)=(5x^2-6)/(3x+8) is (3x+sqrt(9x^2-20(-6-8x)))/(10),(3x-sqrt(9x^2-20(-6-8x)))/(10)