Question

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

gx = x − 3x
hx = 5x + 2
Write the expressions for (g - h)(x) and (g * h)(x) and evaluate (g + h)(−2).

Answer 1

Explanation:

Given the functions g(x) = x − 3x and h(x) = 5x + 2, we are to calculatae for the expression;

a) (g - h)(x) an (g * h)(x)

(g - h)(x) = g(x) - h(x)

(g - h)(x) = x − 3x -(5x+2)

(g-h)(x) = x-3x-5x-2

(g-h)(x) =-7x-2

b) (g * h)(x) = g(x) * h(x)

(g * h)(x) = (x − 3x )(5x+2)

(g * h)(x) = 5x²+2x-15x²-6x

(g * h)(x) = 5x²-15x²+2x-6x

(g * h)(x) = -10x²-4x

c) To get (g + h)(−2), we need to first calculate (g + h)(x) as shown;

(g + h)(x) an (g * h)(x)

(g + h)(x) = g(x) +h(x)

(g + h)(x) = x − 3x + (5x+2)

(g+h)(x) = x-3x+5x+2

(g+h)(x) =3x+2

Substituting x = -2 into the resulting function;

(g+h)(-2) = 3(-2)+2

(g+h)(-2) = -6+2

(g+h)(-2) = -4