What is the inverse of f(x)=(10x)/(x^2+25) ?

The inverse of f(x)=(10x)/(x^2+25) is (5(sqrt(-x^2+1)+1))/x ,(5(-sqrt(-x^2+1)+1))/x

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inverse of f(x)=(10x)/(x^2+25)

inverse

f (x) = \frac{10 x}{x ^{2} + 25}

\frac{5 ( - x ^{2} + 1 + 1 )}{x}, \frac{5 ( - - x ^{2} + 1 + 1 )}{x}

Solution steps

y = \frac{10 x}{x ^{2} + 25}

Replace

x

with

y

x = \frac{10 y}{y ^{2} + 25}

Solve for

y, x = \frac{10 y}{y ^{2} + 25}

\frac{5 ( - x ^{2} + 1 + 1 )}{x}, \frac{5 ( - - x ^{2} + 1 + 1 )}{x}

f (x) = 3 x^{2} + 7

y = - 5 x + 2

\frac{6 - 1}{4 - 2}

f (x) = 5^{3 x - 5}

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

What is the inverse of f(x)=(10x)/(x^2+25) ?
The inverse of f(x)=(10x)/(x^2+25) is (5(sqrt(-x^2+1)+1))/x ,(5(-sqrt(-x^2+1)+1))/x