please help?

Question

if f(x) = (x^2 +1) if x ≤ 0
(-x) if x > 0

and g(x) = (1+x) if x ≤ 1
(2x) if x > 1

what are the expressions for:

1. f + g
2. f ○ g
3. g ○ f

help appreciated

Answer 1

1)

(f + g)(x) = f(x) + g(x)

Case 1: x <= 0 and x <= 1 (which means x <= 0):

= (x^2 + 1) + (1 + x)
= x^2 + x + 2

Case 2: x <= 0 and x >= 1. (Impossible)

Case 3: x > 0 and x <= 1 (which means 0 < x <= 1):

= (-x) + 1 + x
= 1

Case 4: x > 0 and x > 1 (which means x > 1)

= (-x) + 2x
= x

Therefore,
(f + g)(x) = { x^2 + x + 2 if x <= 0
{ 1 if 0 < x <= 1
{ x if x > 1