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

The inverse of f(x)= 3/(sqrt(x)+4) is 9/(x^2)-(24)/x+16

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inverse of f(x)= 3/(sqrt(x)+4)

inverse

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

\frac{9}{x ^{2}} - \frac{24}{x} + 16

Solution steps

y = \frac{3}{x + 4}

Replace

x

with

y

x = \frac{3}{y + 4}

Solve for

y, x = \frac{3}{y + 4}

\frac{9}{x ^{2}} - \frac{24}{x} + 16

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

y = 5^{2 x}

\frac{1}{2 x}

f (x) = - 3 + x^{3}

f (x) = 6 x^{\frac{1}{3}} - 2

What is the inverse of f(x)= 3/(sqrt(x)+4) ?
The inverse of f(x)= 3/(sqrt(x)+4) is 9/(x^2)-(24)/x+16