What is the inverse of f(x)=(-2)/(x+3)+5 ?

The inverse of f(x)=(-2)/(x+3)+5 is (-3x+13)/(x-5)

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inverse of f(x)=(-2)/(x+3)+5

inverse

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

\frac{- 3 x + 13}{x - 5}

Solution steps

y = \frac{- 2}{x + 3} + 5

Replace

x

with

y

x = \frac{- 2}{y + 3} + 5

Solve for

y, x = \frac{- 2}{y + 3} + 5

\frac{- 3 x + 13}{x - 5}

f (x) = \frac{3 - 2 x}{3 x - 2}

f (x) = \frac{9 x}{4 x - 3}

y = \frac{x + 3}{x}

\frac{2 - x}{5}

What is the inverse of f(x)=(-2)/(x+3)+5 ?
The inverse of f(x)=(-2)/(x+3)+5 is (-3x+13)/(x-5)