What is the inverse of f(x)=(7x)/(81-x^2) ?

The inverse of f(x)=(7x)/(81-x^2) is -(7+sqrt(49+324x^2))/(2x),-(7-sqrt(49+324x^2))/(2x)

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inverse of f(x)=(7x)/(81-x^2)

inverse

f (x) = \frac{7 x}{81 - x ^{2}}

- \frac{7 + 49 + 324 x ^{2}}{2 x}, - \frac{7 - 49 + 324 x ^{2}}{2 x}

Solution steps

y = \frac{7 x}{81 - x ^{2}}

Replace

x

with

y

x = \frac{7 y}{81 - y ^{2}}

Solve for

y, x = \frac{7 y}{81 - y ^{2}}

- \frac{7 + 49 + 324 x ^{2}}{2 x}, - \frac{7 - 49 + 324 x ^{2}}{2 x}

f (x) = 11.25 x - 90

f (x) = 9 + 5 x - 9

f (x) = - 1 + 5 - 4 x - x^{2}

f (x) = 5 + 3 x - 3

f (x) = x^{2} - 2 x - 6

What is the inverse of f(x)=(7x)/(81-x^2) ?
The inverse of f(x)=(7x)/(81-x^2) is -(7+sqrt(49+324x^2))/(2x),-(7-sqrt(49+324x^2))/(2x)