G(x)=-x + 4x
h(x)=4x + 2
find (g-)
how do i answer this question

(g - h)(-4x) = 4x - 2

Step-by-step explanation:

This problem is one dealing with "composite functions."  We are given the definitions of functions g(x) and h(x) and are asked to find the difference between g and h, namely, what is left if we subtact h from g.  After having done that, we replace x in this composite function with the input (-4x).

The difference (g - h)(x) is as follows:  g(x) - h(x) = -x + 4x - [4x + 2].

If we simplify the algebra, we get g(x) - h(x) = -x + 4x - [4x + 2] = -x - 2.

Next, substitute -4x for x in this last result.  We get (g - h)(-4x) = 4x - 2.

Please note:  You might want to check out your g(x) = -x + 4x.  Normally we would write this as +3x.  

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for