If f(x) and g(x) are linear functions, the f(x) + g(x) is a linear function.

Answer 1

Suppose f(x) and g(x) are linear functions. This means that each of them can be written in the form, l(x) = ax + b.

Then, define: f(x) = ax + b and g(x) = cx + d.

Adding the two functions together:

f(x) + g(x) = ax + b + cx + d

Rearranging this using the commutative property of addition:

f(x) + g(x) = ax + cx + b + d

Then, we can group terms using the associative property of addition:

f(x) + g(x) = (a + c)x + (b+d)

Let e = a + c and let h = (b+d)

Then,

f(x) + g(x) = ex + h, which is by definition linear.