What is the inverse of f(x)=((x+4))/((x+10)) ?

The inverse of f(x)=((x+4))/((x+10)) is (4-10x)/(x-1)

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inverse of f(x)=((x+4))/((x+10))

inverse

f (x) = \frac{( x + 4 )}{( x + 10 )}

\frac{4 - 10 x}{x - 1}

Solution steps

y = \frac{x + 4}{x + 10}

Replace

x

with

y

x = \frac{y + 4}{y + 10}

Solve for

y, x = \frac{y + 4}{y + 10}

\frac{4 - 10 x}{x - 1}

f (x) = - x - 1 - 1

f (x) = arcsin (2 x - 1)

f (x) = \frac{5}{2} \cdot (1 + π \cdot csch (π))

f (x) = \frac{1}{3 x + 28}

f (x) = \frac{1}{8} x + 7

What is the inverse of f(x)=((x+4))/((x+10)) ?
The inverse of f(x)=((x+4))/((x+10)) is (4-10x)/(x-1)