Question

Suppose that the functions g and h are defined for all real numbers x as follows. g(x) =x-6 h (x) = 2x^2 Write the expressions for (g- h)(x) and (g h)(x) and evaluate (g+h)(-1). (g - h) (x) = (g+h)(-1)=

Answer 1

Explanation:

Given the functions g(x) =x-6 and h(x) = 2x², we are to find the following expression;

a) (g- h)(x)

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

(g- h)(x) = x-6- 2x²

(g- h)(x) = -2x²+x-6

b) (g+ h)(x)

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

(g- h)(x) = x-6+ 2x²

(g- h)(x) = 2x²+x-6

c) To evaluate (g+h)(-1)

(g+h)(-1) = g(-1)+h(-1)

(g+h)(-1) = -1-6+ 2(-1)²

(g+h)(-1) = -7+2(1)

(g+h)(-1) = -5