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{1}{2} x^{2} + 9 x + 8

(- 1) (- 3)

\frac{x ^{2} + 2 x - 3}{x ^{2} - 1}

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

- x^{2} + 4 x + 5

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)