Question

1. consider the functions ( f(x) = x + 3 ) and ( g(x) = -x + 1 ) represented on the right.

a) represent the function ( s ) given that ( s(x) = f(x) + g(x) ).
b) represent the function ( p ) given that ( p(x) = f(x) cdot g(x) ).

Explanation:

Step1: Substitute f, g into s(x)

$s(x) = (x+3) + (-x+1)$

Step2: Simplify s(x)

$s(x) = x + 3 - x + 1 = 4$

Step3: Substitute f, g into p(x)

$p(x) = (x+3) \cdot (-x+1)$

Step4: Expand and simplify p(x)

$p(x) = -x^2 + x - 3x + 3 = -x^2 -2x +3$

Answer:

a) $s(x) = 4$
b) $p(x) = -x^2 -2x + 3$