What is the inverse of f(x)=(5x)/(sqrt(x^2-1)) ?

The inverse of f(x)=(5x)/(sqrt(x^2-1)) is (xsqrt(x^2-25))/(x^2-25),-(xsqrt(x^2-25))/(x^2-25)

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inverse of f(x)=(5x)/(sqrt(x^2-1))

inverse

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

\frac{x x ^{2} - 25}{x ^{2} - 25}, - \frac{x x ^{2} - 25}{x ^{2} - 25}

Solution steps

y = \frac{5 x}{x ^{2} - 1}

Replace

x

with

y

x = \frac{5 y}{y ^{2} - 1}

Solve for

y, x = \frac{5 y}{y ^{2} - 1}

\frac{x x ^{2} - 25}{x ^{2} - 25}, - \frac{x x ^{2} - 25}{x ^{2} - 25}

\frac{3 x + 1}{1 x - 1}

f (x) = \frac{- 3 x + 12}{4}

f (x) = \frac{4 x - 7}{x + 5}

y = \frac{1}{3} x

f (x) = (x + 3) 5 + 9

What is the inverse of f(x)=(5x)/(sqrt(x^2-1)) ?
The inverse of f(x)=(5x)/(sqrt(x^2-1)) is (xsqrt(x^2-25))/(x^2-25),-(xsqrt(x^2-25))/(x^2-25)