Question

Let f(x) = m1x + b1 and g(x) = m2x + b2 be two linear functions.
Answer the following, noting that answers may depend on the the ms and bs.

a. Is f (x) + g(x) a linear function of x?
b. Is f (x) − g(x) a linear function of x?
c. Is f (x) × g(x) a linear function of x?
d. Is f(x)/g(x) a linear function of x?

Answer 1

Why don't you try it with two different functions,
e.g.
f(x) = x+2 , g(x) = 2x - 1

let y = f(x) + g(x)
= x+2 + 2x - 1
= 3x + 1
is this a straight line ?
so what do you think about a) ???

...

c) let y = f(x) * g(x)
= (x+2)(2x-1) = 2x^2 + 3x - 2
Is a quadratic a straight line, that is, a linear function??

etc