EXPLANATION
Given the functions:
g(x) = x+1 and h(x) = 2x^2
First, the expression (g+h)(x) will be as shown as follows:
Assign the function g=x+1
=( x + 1 + h(x) ) (x)
Assign the function h=2x^2
[tex]\mleft(g+h\mright)\mleft(x\mright)=2x^2+x+1[/tex](g*h)(x):
Assign the function g=x+1
=((x+1)h(x))(x)
Assign the function h= 2x^2
=(x+1)*2x^2
Expanding (x+1)*2x^2
=2x^3+2x^2
[tex]\mleft(g\cdot h\mright)\mleft(x\mright)=2x^3+2x^2[/tex](g-h)(-1):
Assign the function g=x+1
=(x+1 -h(x)) (x)
Assign the function h=2x^2
=(x+1-2x^2)(-1)
Evaluating (x+1-2x^2)(-1): -2
=-2
[tex]\mleft(g-h\mright)\mleft(-1\mright)=-2[/tex]
