What is the inverse of f(x)=2+3/(sqrt(5y-4)) ?

The inverse of f(x)=2+3/(sqrt(5y-4)) is (4y^2-16y+25)/(5(y^2-4y+4))

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inverse of f(x)=2+3/(sqrt(5y-4))

inverse

f (x) = 2 + \frac{3}{5 y - 4}

\frac{4 y ^{2} - 16 y + 25}{5 ( y ^{2} - 4 y + 4 )}

Solution steps

x = 2 + \frac{3}{5 y - 4}

Replace

y

with

x

y = 2 + \frac{3}{5 x - 4}

Solve for

x, y = 2 + \frac{3}{5 x - 4}

\frac{4 y ^{2} - 16 y + 25}{5 ( y ^{2} - 4 y + 4 )}

\frac{2 ^{x} - 8}{4 - 2 ^{x}}

3 sin (x) + 3 cos (x)

\frac{5}{x ^{2} + 1}

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

f (x) = 5 + \frac{25}{x}

What is the inverse of f(x)=2+3/(sqrt(5y-4)) ?
The inverse of f(x)=2+3/(sqrt(5y-4)) is (4y^2-16y+25)/(5(y^2-4y+4))