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

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

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inverse of f(x)= x/(x^2-a^2)

inverse

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

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

Solution steps

y = \frac{x}{x ^{2} - a ^{2}}

Replace

x

with

y

x = \frac{y}{y ^{2} - a ^{2}}

Solve for

y, x = \frac{y}{y ^{2} - a ^{2}}

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

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

f (x) = (3 x - 4)

3 x^{2} - 6 x

f (x) = \frac{x - 3}{10 + 2 x}

f (x) = \frac{a ^{x} - 1}{a ^{x} + 1}

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