Question

If 𝑓(𝑥)=2𝑥−1 and 𝑔(𝑥)=3𝑥+1

then

((𝑓+𝑔)∘(𝑓−𝑔))(𝑥)=

Answer 1

((f+g)∘(f-g))(x)

= (f+g)(f-g)
= f(f-g)+g(f-g)
= 2(f-g)-1 + 3(f-g)+1
= 5(f-g)
= 5((2x-1)-(3x+1))
= 5(-x-2)
= -5x-10
or,
f+g = 5x
f-g = -x-2
(f+g)∘(f-g) = 5(-x-2) = -5x-10