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

The inverse of f(x)=((x+3))/((x+5)) is (3-5x)/(x-1)

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

inverse

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

\frac{3 - 5 x}{x - 1}

Solution steps

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

Replace

x

with

y

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

Solve for

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

\frac{3 - 5 x}{x - 1}

f (x) = \frac{5 + x ^{2}}{4}

f (x) = 48 x^{2} - 36

f (x) = 4 (9)^{2} + 5

\frac{12}{x ^{2} - 25} - 3

(3 x + 1)^{2}

What is the inverse of f(x)=((x+3))/((x+5)) ?
The inverse of f(x)=((x+3))/((x+5)) is (3-5x)/(x-1)