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

The inverse of f(x)= 1/(sqrt(x)+5) is 1/(x^2)-(10)/x+25

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inverse of f(x)= 1/(sqrt(x)+5)

inverse

f (x) = \frac{1}{x + 5}

\frac{1}{x ^{2}} - \frac{10}{x} + 25

Solution steps

y = \frac{1}{x + 5}

Replace

x

with

y

x = \frac{1}{y + 5}

Solve for

y, x = \frac{1}{y + 5}

\frac{1}{x ^{2}} - \frac{10}{x} + 25

\frac{3 x + 10}{x + 3}

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

\frac{2 + 4 x}{- 4 - 5 x}

y = \frac{( 3 x - 7 )}{( 9 x + 1 )}

z^{- 1} (\frac{2 z}{( z - 2 ) ^{2}})

What is the inverse of f(x)= 1/(sqrt(x)+5) ?
The inverse of f(x)= 1/(sqrt(x)+5) is 1/(x^2)-(10)/x+25