Operations with Functions - h(x)=-2x,g(x)=3x+1 Find (h+g)(x/2)

Question

The answer choices are

A)x^2+1

B)x-1

C)x+2/2

D)-x+2/2

 

I picked A as the right answer but I'm not sure. 

Answer 1

Two approaches: (note we are adding two functions, and composing a third, x/2. It might help to rewrite h and g using u instead of x first, so as not to confuse with the x in the input x/2: this gives h(u)=-2u, and g(u)=3u+1)

 

1. Combine h and g second:

h(x/2) = -2*(x/2) = -x

g(x/2) = 3*(x/2) + 1 = (3x+2)/2

 

Now (h + g)(x/2) = -x + (3x+2)/2

                           = (-2x + 3x + 2)/2

                           = (x+2)/2

 

OR

2. Combine h and g first:

(h+g)(u) = -2u + 3u + 1 = u + 1

 

Now (h + g)(x/2) = (x/2) + 1 = (x+2)/2

 

Note here I used u instead of x, but you can just replace the u's with x's to match the problem as given.