What is the inverse of f(x)=((3x+10))/(4-5x) ?

The inverse of f(x)=((3x+10))/(4-5x) is -(10-4x)/(3+5x)

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inverse of f(x)=((3x+10))/(4-5x)

inverse

f (x) = \frac{( 3 x + 10 )}{4 - 5 x}

- \frac{10 - 4 x}{3 + 5 x}

Solution steps

y = \frac{3 x + 10}{4 - 5 x}

Replace

x

with

y

x = \frac{3 y + 10}{4 - 5 y}

Solve for

y, x = \frac{3 y + 10}{4 - 5 y}

- \frac{10 - 4 x}{3 + 5 x}

What is the inverse of f(x)=((3x+10))/(4-5x) ?
The inverse of f(x)=((3x+10))/(4-5x) is -(10-4x)/(3+5x)