What is the inverse of f(x)=((x+6))/((x+16)) ?

The inverse of f(x)=((x+6))/((x+16)) is (6-16x)/(x-1)

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inverse of f(x)=((x+6))/((x+16))

inverse

f (x) = \frac{( x + 6 )}{( x + 16 )}

\frac{6 - 16 x}{x - 1}

Solution steps

y = \frac{x + 6}{x + 16}

Replace

x

with

y

x = \frac{y + 6}{y + 16}

Solve for

y, x = \frac{y + 6}{y + 16}

\frac{6 - 16 x}{x - 1}

f (x) = - x + 9

- \frac{1}{2} \cdot ln (1 - 2 y)

f (x) = f (x) = x + 3

+ 11 - 4 x

- 5 x - 5 + 5

What is the inverse of f(x)=((x+6))/((x+16)) ?
The inverse of f(x)=((x+6))/((x+16)) is (6-16x)/(x-1)