Question

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

f(x) = x + 1
g(x) = 4x + 2
Write the expressions for (f times g)(x) and (f-g)(x) and evaluate (f+g)(3).

Answer 1

a) 4x^2 +6x + 2

b) -3x - 1

c) 18

Explanation:

f(x) = x + 1

g(x) = 4x + 2

a) (f*g)(x)

= f(x) * g(x)

= (x + 1) (4x + 2)

= 4x^2 + 2x +4x + 2

= 4x^2 + 6x + 2

b) (f-g) (x)

= f(x) - g(x)

= (x + 1) - (4x + 2)

= x + 1 - 4x - 2

= x - 4x + 1 - 2

= -3x - 1

c) (f+g)(3)

= (f+g)(x) = f(x) + g(x)

= (x + 1) + (4x + 2)

= x + 1 + 4x + 2

= x + 4x + 1 + 2

= 5x + 3

put x =3

= 5(3) + 3

= 15 + 3

= 18

Answer 2

1) (fg)(x) = 4x^2 + 6x + 2

2) (f-g)(x) = -3x -1

3) (f+g)(3) = 18

Explanation:

Given:

f(x) = x+1

g(x) = 4x + 2

1) To find (fg)(x)

(fg)(x) = f(x) * g(x)

= (x+1)(4x+2)

= (4x^2 +2x+4x+2)

(fg)(x) = 4x^2 + 6x + 2

2) To find (f-g)(x)

(f-g)(x) = f(x) - g(x)

= (x+1) - (4x+2)

(f-g)(x) = -3x -1

3) To find (f+g)(3)

(f+g)(x) = f(x) + g(x)

(f+g)(3) = f(3) + g(3)

= (3+1) + (4(3)+2)

(f+g)(3) = 18