What is the domain of f(x)=sqrt((16)/(x^2)-1)+25 ?

The domain of f(x)=sqrt((16)/(x^2)-1)+25 is -4<= x<0\lor 0<x<= 4

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domain of f(x)=sqrt((16)/(x^2)-1)+25

domain

f (x) = \frac{16}{x ^{2}} - 1 + 25

- 4 \leq x < 0 or 0 < x \leq 4

Interval Notation

[- 4, 0) \cup (0, 4]

Solution steps

Find non-negative values for radicals:

- 4 \leq x < 0 or 0 < x \leq 4

Find undefined (singularity) points:

x = 0

Combine real regions and undefined points for final function domain

- 4 \leq x < 0 or 0 < x \leq 4

f (x) = - 3 x ln (x)

f (x) = \frac{3 x ^{2}}{x ^{2} - 2 x - 35}

\frac{3 x - 3}{x ( x - 1 )}

ln (\frac{x + 4}{4 x - 16})

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

What is the domain of f(x)=sqrt((16)/(x^2)-1)+25 ?
The domain of f(x)=sqrt((16)/(x^2)-1)+25 is -4<= x<0\lor 0<x<= 4