What is the domain of f(x)=sqrt(36-x^2)+sqrt(x^2-25) ?

The domain of f(x)=sqrt(36-x^2)+sqrt(x^2-25) is -6<= x<=-5\lor 5<= x<= 6

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domain of f(x)=sqrt(36-x^2)+sqrt(x^2-25)

domain

f (x) = 36 - x^{2} + x^{2} - 25

- 6 \leq x \leq - 5 or 5 \leq x \leq 6

Interval Notation

[- 6, - 5] \cup [5, 6]

Solution steps

Find non-negative values for radicals:

- 6 \leq x \leq - 5 or 5 \leq x \leq 6

The function domain

- 6 \leq x \leq - 5 or 5 \leq x \leq 6

What is the domain of f(x)=sqrt(36-x^2)+sqrt(x^2-25) ?
The domain of f(x)=sqrt(36-x^2)+sqrt(x^2-25) is -6<= x<=-5\lor 5<= x<= 6