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

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

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

inverse

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

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

Solution steps

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

Replace

x

with

y

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

Solve for

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

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

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

f (x) = - 5^{x}

y = 4 x - 4

(4, 1), (- 2, - 3)

f (x) = - x^{3} + 9 x^{2} - 2

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