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

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

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

inverse

f (x) = \frac{5 x + 1}{- x + 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 ^{3} + 4 x ^{2}}{7 x ^{2} - 2}

y = - x + 8

2 x^{2} - 4 x - 1

f (x) = 8 x^{3} + 7

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