What is the inverse of f(x)=((3x+7))/((2x-5)) ?

The inverse of f(x)=((3x+7))/((2x-5)) is (7+5x)/(2x-3)

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inverse of f(x)=((3x+7))/((2x-5))

inverse

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

\frac{7 + 5 x}{2 x - 3}

Solution steps

y = \frac{3 x + 7}{2 x - 5}

Replace

x

with

y

x = \frac{3 y + 7}{2 y - 5}

Solve for

y, x = \frac{3 y + 7}{2 y - 5}

\frac{7 + 5 x}{2 x - 3}

f (x) = x^{2} - 10 x + 21

- x + 16 - x

\frac{3 x}{7 x - 3}

f (x) = \frac{( - 2 x - 7 )}{( 6 x + 8 )}

f (x) = \frac{x ^{2}}{4} - 1

What is the inverse of f(x)=((3x+7))/((2x-5)) ?
The inverse of f(x)=((3x+7))/((2x-5)) is (7+5x)/(2x-3)