What is the domain of f(x)=(x+6)/(24-sqrt(x^2-49)) ?

The domain of f(x)=(x+6)/(24-sqrt(x^2-49)) is x 25

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domain of f(x)=(x+6)/(24-sqrt(x^2-49))

domain

f (x) = \frac{x + 6}{24 - x ^{2} - 49}

x < - 25 or - 25 < x \leq - 7 or 7 \leq x < 25 or x > 25

Interval Notation

(- \infty, - 25) \cup (- 25, - 7] \cup [7, 25) \cup (25, \infty)

Solution steps

Find non-negative values for radicals:

x \leq - 7 or x \geq 7

Find undefined (singularity) points:

x = 25, x = - 25

Combine real regions and undefined points for final function domain

x < - 25 or - 25 < x \leq - 7 or 7 \leq x < 25 or x > 25

y = sin (x) + 2

- 3 x^{2} + x + 5

2 cos (2 x - 1) + 4

- 6 cos (8 x - \frac{π}{2})

What is the domain of f(x)=(x+6)/(24-sqrt(x^2-49)) ?
The domain of f(x)=(x+6)/(24-sqrt(x^2-49)) is x<-25\lor-25<x<=-7\lor 7<= x<25\lor x>25