What is the domain of f(x)=sqrt((|x-1|-2)/(3-|x-4|)) ?

The domain of f(x)=sqrt((|x-1|-2)/(3-|x-4|)) is -1<= x<1\lor 3<= x<7

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domain of f(x)=sqrt((|x-1|-2)/(3-|x-4|))

domain

f (x) = \frac{∣ x - 1 ∣ - 2}{3 - ∣ x - 4 ∣}

- 1 \leq x < 1 or 3 \leq x < 7

Interval Notation

[- 1, 1) \cup [3, 7)

Solution steps

Find non-negative values for radicals:

- 1 \leq x < 1 or 3 \leq x < 7

Find undefined (singularity) points:

x = 1, x = 7

Combine real regions and undefined points for final function domain

- 1 \leq x < 1 or 3 \leq x < 7

e^{x + 1} + 1

250 \cdot e^{(0.0228 \cdot 8)}

f (x) = \frac{( x - 4 )}{x - 8}

g (x) = \frac{x ^{2}}{x ^{2} + 4}

f (x) = 7 + 4 x

What is the domain of f(x)=sqrt((|x-1|-2)/(3-|x-4|)) ?
The domain of f(x)=sqrt((|x-1|-2)/(3-|x-4|)) is -1<= x<1\lor 3<= x<7