SUM DIFFERENCE PRODUCT AND QUOTIENT OF FUNCTIONS

Find

(i)  (f + g)(x)

(ii)  (f – g)(x)

and state the domain of each. Then evaluate f + g and f - g for the given value of x.

Problem 1 :

f(x) = -5∜x, g(x) = 19∜x; x = 16

Solution :

Given, f(x) = -5∜x and g(x) = 19∜x

x = 16

(i)  (f + g)(x) = f(x) + g(x)

(f + g)(x) = -5∜x + 19∜x

(f + g)(x) = 14∜x

When x = 16,

(f + g)(16) = 14∜16

= 14∜(2 ⋅ 2 ⋅ 2 ⋅ 2)

(f + g)(16) = 14(2)

(ii)  (f - g)(x) = f(x) - g(x)

=  -5∜x - 19∜x

(f - g)(x) = = -24∜x

(f - g)(16) = -24∜16

= -24∜2 ⋅ 2 ⋅ 2 ⋅ 2

(f - g)(16) = -24(2)

(f - g)(16) = -48

Domain is set of all positive values.

Problem 2 :

f(x) = ∛2x, g(x) = -11∛2x; x = -4

Solution :

Given, f(x) = ∛2x and  g(x) = -11∛2x

 x = -4

(i)  (f + g)(x) = f(x) + g(x)

(f + g)(x) = ∛2x + (-11∛2x)

(f + g)(x) = -10∛2x

When, x = -4

(f + g)(-4) = -10∛2(-4)

= -10∛(-8)

= 10∛(-2 ⋅ -2 ⋅ -2)

= 10(-2)

(f + g)(-4) = -20

(ii)  (f - g)(x) = f(x) - g(x)

(f - g)(x) = ∛2x - (-11∛2x)

(f - g)(x) = 12∛2x

(f - g)(-4) = 12∛2(-4)

= 12∛(-8)

= -12∛(-2 ⋅ -2 ⋅ -2)

(f - g)(-4) = -12(-2)

(f - g)(-4) = 24

Problem 3 :

If f(x) = -7x + 2 and g(x) = x³ + x², find (g · f)(x).

Solution:

(g · f)(x) = g(x)·f(x)

(g · f)(x) = (x³ + x²) · (-7x + 2)

= -7x⁴ + 2x³ - 7x³ + 2x²

= -7x⁴ - 5x³ + 2x²

Problem 4 :

If f(x) = 2x - 6 and g(x) = x² - 5x + 6, find f(x)/g(x).

Solution: