Let f(x) = 2x + 5 and g(x) = x2 + x. Describe (iii) fg (iv) f/g Find the domain in each case.

Solution:

(iii) fg

We know that: (fg)(x) = f(x)g(x)

(fg)(x) is defined for x belonging to R. Therefore, the domain of fg is R

(iv) f/g

We know that:

(f/g) (x) is defined for all real values of x, except for the case when x² + x = 0.

x = 0 or –1

When x = 0 or –1, The outcome of the division will be ambiguous, hence (f/g) (x)will be undefined.

∴ The domain of f/g = R – {–1, 0}