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

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

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

inverse

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

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

Solution steps

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

Replace

x

with

y

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

Solve for

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

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

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