Question #bd4c8

2 Answers
Nov 2, 2017

9x^2+6x+2

Explanation:

First, we need to know that (g @ h)(x)=g[h(x)]

In this question, we have to sub h(x) into it, then, replace the x of g(x) by the value of h(x) as the following:

(g @ h)(x)=g[h(x)]
=g(3x+1)
=(3x+1)^2+1
=(3x)^2+2*3x*1+1^2+1
=9x^2+6x+1+1
=9x^2+6x+2

Here is the answer. Hope this can help you :)

Nov 2, 2017

An alternative notation for, (g@h)(x), is g(h(x)); the latter notation clearly illustrates that one should substitute h(x) for every instance of x within g(x).

Explanation:

Start with g(x):

g(x) = x^2+1

Substitute h(x) for every x within g(x)

g(h(x)) = (h(x))^2+1

One right side of g(x), substitute the right side of h(x) for every instance of h(x):

g(h(x)) = (3x+1)^2+1

Technically, we are done but it is better to simplify the equation:

g(h(x)) = 9x^2+ 6x+2

Returning to the other notation:

(g@h)(x)= 9x^2+ 6x+2