Question

Algebraically show that each of the given combinations are equivalent to the given functions. f(x) – g() is

equivalent to m(x) given:
f(0)
= - 3x + 5; g(x)
- 5x – 7; m(x) = 2x + 12
f(x) – g(x) = (
=
Is f(x) – g(x) equivalent to m(x)? yes

Answer 1

`f(x) - g(x) = 2x + 12`

`m(x) = f(x) - g(x)` --- True

Explanation:

Given

`f(x) = -3x + 5`

`g(x) = -5x - 7`

`m(x) = 2x + 12`

Solving (a):
`f(x) - g(x)`

From the given parameters, we have:

`f(x) = -3x + 5`

`g(x) = -5x - 7`

So:

`f(x) - g(x)=-3x+5 + 5x + 7`

Collect like terms

`f(x) - g(x) = 2x + 12`

Solving (b) m(x) = f(x) = g(x)?

In (a), we have:

`f(x) - g(x) = 2x + 12`

And

`m(x) = 2x + 12` --- given

By comparison:

`m(x) = f(x) - g(x)`