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

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

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

inverse

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

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

Solution steps

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

Replace

x

with

y

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

Solve for

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

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

f (x) = 4 - x^{2} - 2 x

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

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

+ x^{2} - 8 x + 15

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

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