sum, difference, and product of two functions

Question

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

g(x)=2x

h(x)= 4x^2 

 

Write expressions for 

(g + h)(x)= ___

(the "." is supposed to be for multiplication)

(g . h)(x) = ___

(g - h)(-1)=_____

 

Thank you so much!! :D 

Answer 1

G +h = 4x^2 + 2x

 

g * h = 8x^3

 

g-h = 2x - 4x^2

So (g-h)(-1) =  2(-1) - 4(-1)^2 = 2(-1) - 4(1) = -2 - 4 = -6

Note that g(-1) = -2 and h(-1) = 4 and -2 - 4 = -6

 

 

Answer 2

g(x) = 2x and h(x) = 4x²

(g+h)(x) = 2x + 4x² = 4x² + 2x

(g•h)(x) = 2x(4x²) = 8x³

(g-h)(x) = 2x - 4x² = -4x² + 2

(g-h)(-1) = -4(-1)² + 2 = -4 + 2 = -2