Question

Suppose that the functions g and h are defined for all real numbers x as follows.g(x)=x²h(x) = 4xWrite the expressions for (h-g)(x) and (h.g)(x) and evaluate (h+g)(2).

Answer 1

we have the functions

g(x)=x^2

h(x)=4x^3

so

Part 1

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

substitute given values

4x^3-x^2

answer part 1 is 4x^3-x^2

Part 2

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

substitute

4x^3*x^2=4x^5

answer part 2 is 4x^5

Part 3

(h+g)(2)=h(2)+g(2)

we have that

h(2)=4(2)^3=32

g(2)=(2)^2=4

therefore

(h+g)(2)=32+4=36