What is the inverse of f(x)= 1/(sqrt(x+4)) ?

The inverse of f(x)= 1/(sqrt(x+4)) is 1/(x^2)-4

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inverse of f(x)= 1/(sqrt(x+4))

inverse

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

\frac{1}{x ^{2}} - 4

Solution steps

y = \frac{1}{x + 4}

Replace

x

with

y

x = \frac{1}{y + 4}

Solve for

y, x = \frac{1}{y + 4}

\frac{1}{x ^{2}} - 4

f (x) = (x + \frac{3}{2})^{2} - \frac{37}{4}

f (x) = \frac{1}{x ^{2}}, x < 0

f (x) = \frac{6}{( x + 5 )}

y = \frac{5 x - 8}{9 x + 6}

53. 7^{x - 0.7} + 2

What is the inverse of f(x)= 1/(sqrt(x+4)) ?
The inverse of f(x)= 1/(sqrt(x+4)) is 1/(x^2)-4