What is the inverse of f(x)=(x+4)/(x+14) ?

The inverse of f(x)=(x+4)/(x+14) is (4-14x)/(x-1)

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inverse of f(x)=(x+4)/(x+14)

inverse

f (x) = \frac{x + 4}{x + 14}

\frac{4 - 14 x}{x - 1}

Solution steps

y = \frac{x + 4}{x + 14}

Replace

x

with

y

x = \frac{y + 4}{y + 14}

Solve for

y, x = \frac{y + 4}{y + 14}

\frac{4 - 14 x}{x - 1}

y = \frac{x ^{2}}{x ^{2} + 1}

f (x) = \frac{5 x + 1}{2 x + 3}

f (x) = \frac{x ^{2} + 1}{x ^{4} + 3 x ^{2} + 1}

y = 4 x^{2} + 34 x

f (x) = x (500 - 2 x)

What is the inverse of f(x)=(x+4)/(x+14) ?
The inverse of f(x)=(x+4)/(x+14) is (4-14x)/(x-1)