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

The inverse of f(x)=(4-x)/(x-10) is (4+10x)/(x+1)

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inverse of f(x)=(4-x)/(x-10)

inverse

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

\frac{4 + 10 x}{x + 1}

Solution steps

y = \frac{4 - x}{x - 10}

Replace

x

with

y

x = \frac{4 - y}{y - 10}

Solve for

y, x = \frac{4 - y}{y - 10}

\frac{4 + 10 x}{x + 1}

f (x) = 6 x + 8 - 5, x \geq - 8

y = 6 (x^{- \frac{1}{4}})

f (x) = \frac{5 x - 1}{4 x + 7}

f (x) = \frac{8}{y + 3}

f (x) = - 2 x + 1 - 5

What is the inverse of f(x)=(4-x)/(x-10) ?
The inverse of f(x)=(4-x)/(x-10) is (4+10x)/(x+1)