What is the domain of f(x)=sqrt(x+1)-(sqrt(7-x))/x ?

The domain of f(x)=sqrt(x+1)-(sqrt(7-x))/x is -1<= x<0\lor 0<x<= 7

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domain of f(x)=sqrt(x+1)-(sqrt(7-x))/x

domain

f (x) = x + 1 - \frac{7 - x}{x}

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

Interval Notation

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

Solution steps

Find non-negative values for radicals:

- 1 \leq x \leq 7

Find undefined (singularity) points:

x = 0

Combine real regions and undefined points for final function domain

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

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

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

(13, 2), (7, 10)

t + 1

y = 2 x + 1

What is the domain of f(x)=sqrt(x+1)-(sqrt(7-x))/x ?
The domain of f(x)=sqrt(x+1)-(sqrt(7-x))/x is -1<= x<0\lor 0<x<= 7