Question

Can someone help me answer this?

Answer 1

Answer:

The function f(x) has a hole at point x = - 5.

Step-by-step explanation:

We are given a function as

$f(x) = \frac{x^{2} + 7x + 10}{x^{2} + 9x + 20}$

Now, we have to describe where the function has a hole.

Now, $f(x) = \frac{x^{2} + 7x + 10}{x^{2} + 9x + 20}$

⇒ $f(x) = \frac{(x + 5)(x + 2)}{(x + 4)(x + 5)}$

Therefore, the common factor of the numerator and denominator is (x + 5).

Now, (x + 5) = 0

⇒ x = - 5

Therefore, the function f(x) has a hole at point x = - 5. (Answer)