What is the inverse of f(x)=(2x)/(sqrt(x^2+3)) ?

The inverse of f(x)=(2x)/(sqrt(x^2+3)) is sqrt(-(3x^2)/(x^2-4)),-sqrt(-(3x^2)/(x^2-4))

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inverse of f(x)=(2x)/(sqrt(x^2+3))

inverse

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

- \frac{3 x ^{2}}{x ^{2} - 4}, - - \frac{3 x ^{2}}{x ^{2} - 4}

Solution steps

y = \frac{2 x}{x ^{2} + 3}

Replace

x

with

y

x = \frac{2 y}{y ^{2} + 3}

Solve for

y, x = \frac{2 y}{y ^{2} + 3}

- \frac{3 x ^{2}}{x ^{2} - 4}, - - \frac{3 x ^{2}}{x ^{2} - 4}

What is the inverse of f(x)=(2x)/(sqrt(x^2+3)) ?
The inverse of f(x)=(2x)/(sqrt(x^2+3)) is sqrt(-(3x^2)/(x^2-4)),-sqrt(-(3x^2)/(x^2-4))