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

The inverse of f(x)= t/(t^2-4) is (1+sqrt(1+16t^2))/(2t),(1-sqrt(1+16t^2))/(2t)

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

inverse

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

\frac{1 + 1 + 16 t ^{2}}{2 t}, \frac{1 - 1 + 16 t ^{2}}{2 t}

Solution steps

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

Replace

t

with

x

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

Solve for

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

\frac{1 + 1 + 16 t ^{2}}{2 t}, \frac{1 - 1 + 16 t ^{2}}{2 t}

What is the inverse of f(x)= t/(t^2-4) ?
The inverse of f(x)= t/(t^2-4) is (1+sqrt(1+16t^2))/(2t),(1-sqrt(1+16t^2))/(2t)