What is the inverse of f(x)=(5x+1)/(-x+7),x\ne 7 ?

The inverse of f(x)=(5x+1)/(-x+7),x\ne 7 is -(1-7x)/(5+x)

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inverse of f(x)=(5x+1)/(-x+7),x\ne 7

inverse

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

- \frac{1 - 7 x}{5 + x}

Solution steps

y = \frac{5 x + 1}{- x + 7}

Replace

x

with

y

x = \frac{5 y + 1}{- y + 7}

Solve for

y, x = \frac{5 y + 1}{- y + 7}

- \frac{1 - 7 x}{5 + x}

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

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

y = (\frac{( 1 + x )}{1 - x})

(x - 9)^{2} + 3

What is the inverse of f(x)=(5x+1)/(-x+7),x\ne 7 ?
The inverse of f(x)=(5x+1)/(-x+7),x\ne 7 is -(1-7x)/(5+x)