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

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

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

domain

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

- 2 \leq x < 1 or 1 < x \leq 2

Interval Notation

[- 2, 1) \cup (1, 2]

Solution steps

Find non-negative values for radicals:

- 2 \leq x \leq 2

Find undefined (singularity) points:

x = 1

Combine real regions and undefined points for final function domain

- 2 \leq x < 1 or 1 < x \leq 2

f (x) = 4 (2^{- 2 x + 7}) - 5

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

- x^{2} + x - 2

(\frac{1}{2})^{x} + 3

\frac{x - 3}{x ^{2}}

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