Question

Suppose that the functions and g are defined for all real numbers x as follows.

f(x)=x+6
g(x) = 2x + 6
Write the expressions for (f-g)(x) and (fg)(x) and evaluate (f+g)(1).

Answer 1

Explanation:

Given functions are,

f(x) = x + 6

g(x) = 2x + 6

(f - g)(x) = (x + 6) - (2x + 6)

= -x

(f . g)(x) = f(x) × g(x)

= (x + 6)(2x + 6)

= 2x² + 6x + 12x + 36

= 2x² + 18x + 36

(f + g)(x) = (x + 6) + (2x + 6)

= 3x + 12

(f + g)(1) = 3(1) + 12

= 15