What is the domain of f(x)=(x^2+14x+49)/(49-x^2) ?

The domain of f(x)=(x^2+14x+49)/(49-x^2) is x 7

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domain of f(x)=(x^2+14x+49)/(49-x^2)

domain

f (x) = \frac{x ^{2} + 14 x + 49}{49 - x ^{2}}

x < - 7 or - 7 < x < 7 or x > 7

Interval Notation

(- \infty, - 7) \cup (- 7, 7) \cup (7, \infty)

Solution steps

Find undefined (singularity) points:

x = 7, x = - 7

The function domain

x < - 7 or - 7 < x < 7 or x > 7

(x - 3) (x + 2)

(x + 3) (x + 2)

- 1 \cdot (- 1)

\frac{15}{4}

\frac{11}{2}

What is the domain of f(x)=(x^2+14x+49)/(49-x^2) ?
The domain of f(x)=(x^2+14x+49)/(49-x^2) is x<-7\lor-7<x<7\lor x>7