What is the inverse of f(x)=(x^2-2x-15)/(x^2-4) ?

The inverse of f(x)=(x^2-2x-15)/(x^2-4) is (1+sqrt(4x^2-19x+16))/(1-x),(1-sqrt(4x^2-19x+16))/(1-x)

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inverse of f(x)=(x^2-2x-15)/(x^2-4)

inverse

f (x) = \frac{x ^{2} - 2 x - 15}{x ^{2} - 4}

\frac{1 + 4 x ^{2} - 19 x + 16}{1 - x}, \frac{1 - 4 x ^{2} - 19 x + 16}{1 - x}

Solution steps

y = \frac{x ^{2} - 2 x - 15}{x ^{2} - 4}

Replace

x

with

y

x = \frac{y ^{2} - 2 y - 15}{y ^{2} - 4}

Solve for

y, x = \frac{y ^{2} - 2 y - 15}{y ^{2} - 4}

\frac{1 + 4 x ^{2} - 19 x + 16}{1 - x}, \frac{1 - 4 x ^{2} - 19 x + 16}{1 - x}

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

f (x) = x^{2} - 9, x > 0

f (x) = \frac{1}{4} ln (\frac{1}{3} x)

f (x) = \frac{2 e ^{x} - 10}{22 e ^{x} + 14}

y = 0.0292 \cdot x^{2} + 1.067 \cdot x + 1

What is the inverse of f(x)=(x^2-2x-15)/(x^2-4) ?
The inverse of f(x)=(x^2-2x-15)/(x^2-4) is (1+sqrt(4x^2-19x+16))/(1-x),(1-sqrt(4x^2-19x+16))/(1-x)