Let f(x) = x² - 16 and g(x) = x + 4. Find f/g and its domain.

Solution:

It is given that

f(x) = x² - 16

g(x) = x + 4

Using the algebraic identity (a² - b²) = (a + b)(a - b)

f(x) = x² - 16 = (x + 4)(x - 4)

We know that

(f/g) (x) = [(x + 4)(x - 4)]/ (x + 4)

So we get

(f/g) (x) = x - 4

Here x - 4 is linear and defined for all x.

The domain of this function and any linear function is x ∈ R.

Therefore, f/g is (x - 4) and its domain is x ∈ R.

Let f(x) = x² - 16 and g(x) = x + 4. Find f/g and its domain.

Summary:

Let f(x) = x² - 16 and g(x) = x + 4. f/g is (x - 4) and its domain is x ∈ R.