What is the inverse of f(x)=((x+5))/(x-4) ?

The inverse of f(x)=((x+5))/(x-4) is (5+4x)/(x-1)

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inverse of f(x)=((x+5))/(x-4)

inverse

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

\frac{5 + 4 x}{x - 1}

Solution steps

y = \frac{x + 5}{x - 4}

Replace

x

with

y

x = \frac{y + 5}{y - 4}

Solve for

y, x = \frac{y + 5}{y - 4}

\frac{5 + 4 x}{x - 1}

y = (x - 8) (x + 2)

f (x) = 7 - 2 (x - 1)^{2}

y = \frac{x + 1}{x ^{2} - 4}

y = x + 5

g (x) = x^{2} - 9

What is the inverse of f(x)=((x+5))/(x-4) ?
The inverse of f(x)=((x+5))/(x-4) is (5+4x)/(x-1)