If f(x) = x + 2, g(x) = x - 4, (fg)(x) = ?

Solution:

If f and g are any two real functions then f + g, f - g fg, and f/g are called algebra of the functions. Where we add, subtract, multiply and divide the function .

Given, f(x) = x + 2, g(x) = x - 4

We have (fg)(x) = f(x).g(x)

= (x + 2)(x - 4)

= x² - 4x + 2x - 8

= x² - 2x - 8

Example: If f(x)= x² - 4 and g(x) = 2x + 5 then find (f + g)(x) , (f - g)(x) , (fg)(x), (f/g)(x)

Given, f(x)= x² - 4 and g(x) = 2x + 5

(f + g)(x) = f(x) + g(x) = x² - 4 + 2x + 5 = x² + 2x +1

(f - g)(x) = f(x) - g(x) = x² - 4 - (2x +5) = x² - 2x - 9

(fg)(x) = f(x) . g(x) = (x² - 4)(2x + 5) = 2x³ + 5x² - 8x - 20

(f/g)(x) = f(x) /g(x) =(x² - 4)/(2x + 5) for all x ≠ -(5/2)

If f(x) = x + 2, g(x) = x - 4, (fg)(x) = ?

Summary:

If f(x) = x + 2 and g(x) = x - 4 then (fg)(x) = x² - 2x - 8