What is the inverse of f(x)=(2x+3)/(4-x) ?

The inverse of f(x)=(2x+3)/(4-x) is -(3-4x)/(2+x)

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inverse of f(x)=(2x+3)/(4-x)

inverse

f (x) = \frac{2 x + 3}{4 - x}

- \frac{3 - 4 x}{2 + x}

Solution steps

y = \frac{2 x + 3}{4 - x}

Replace

x

with

y

x = \frac{2 y + 3}{4 - y}

Solve for

y, x = \frac{2 y + 3}{4 - y}

- \frac{3 - 4 x}{2 + x}

f (x) = \frac{3 x}{5 x - 6}

f (x) = 15 x^{3} - 15

f (x) = (9 - x^{2})^{\frac{1}{2}}

\frac{1}{x - 4} - 6

f (x) = \frac{2}{x - 4} + 1

What is the inverse of f(x)=(2x+3)/(4-x) ?
The inverse of f(x)=(2x+3)/(4-x) is -(3-4x)/(2+x)