What is the domain of f(x)=sqrt(x+6)-(sqrt(7-x))/x ?

The domain of f(x)=sqrt(x+6)-(sqrt(7-x))/x is -6<= x<0\lor 0<x<= 7

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domain of f(x)=sqrt(x+6)-(sqrt(7-x))/x

domain

f (x) = x + 6 - \frac{7 - x}{x}

- 6 \leq x < 0 or 0 < x \leq 7

Interval Notation

[- 6, 0) \cup (0, 7]

Solution steps

Find non-negative values for radicals:

- 6 \leq x \leq 7

Find undefined (singularity) points:

x = 0

Combine real regions and undefined points for final function domain

- 6 \leq x < 0 or 0 < x \leq 7

f (x) = lo g_{4} (x - 1)

x^{3} - 27

f (x) = 3 x^{4} - 4 x^{3} + 6

1 + x

(1, 2), (- 1, 3)

What is the domain of f(x)=sqrt(x+6)-(sqrt(7-x))/x ?
The domain of f(x)=sqrt(x+6)-(sqrt(7-x))/x is -6<= x<0\lor 0<x<= 7