What is the domain of f(x)=(sqrt(4-x^2))/(x^2+6x-7) ?

The domain of f(x)=(sqrt(4-x^2))/(x^2+6x-7) is -2<= x<1\lor 1<x<= 2

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domain of f(x)=(sqrt(4-x^2))/(x^2+6x-7)

domain

f (x) = \frac{4 - x ^{2}}{x ^{2} + 6 x - 7}

- 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, x = - 7

Combine real regions and undefined points for final function domain

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

\frac{- 2 - 3 x}{x - 1}

- x + 9

f (x) = \frac{x}{x ^{2} - 4 x + 3}

y = \frac{3 x ^{2} - 3 x}{x ^{2} + x - 12}

\frac{- 7}{2 x ^{\frac{3}{2}}}

What is the domain of f(x)=(sqrt(4-x^2))/(x^2+6x-7) ?
The domain of f(x)=(sqrt(4-x^2))/(x^2+6x-7) is -2<= x<1\lor 1<x<= 2