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

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

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

inverse

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

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

Solution steps

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

Replace

x

with

y

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

Solve for

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

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

f (x) = \frac{x + 6}{x - 5}

f (x) = \frac{( x + 3 ) ^{\frac{1}{4}}}{9}

3 x - y + y

f (x) = - y^{2}

f (x) = \frac{3}{x ^{2} - 81}

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