What is the inverse of f(x)=((3x+4))/(-5x-7) ?

The inverse of f(x)=((3x+4))/(-5x-7) is -(4+7x)/(3+5x)

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inverse of f(x)=((3x+4))/(-5x-7)

inverse

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

- \frac{4 + 7 x}{3 + 5 x}

Solution steps

y = \frac{3 x + 4}{- 5 x - 7}

Replace

x

with

y

x = \frac{3 y + 4}{- 5 y - 7}

Solve for

y, x = \frac{3 y + 4}{- 5 y - 7}

- \frac{4 + 7 x}{3 + 5 x}

5 x = 2 y + 10

f (x) = 7 x^{2} - 8 x

f (x) = x^{4} - 8 x^{2} + 1

y = - \frac{1}{2} x - 4

f (x) = x + y = 4

What is the inverse of f(x)=((3x+4))/(-5x-7) ?
The inverse of f(x)=((3x+4))/(-5x-7) is -(4+7x)/(3+5x)