algebra 2 high school

Question

Suppose f(x)=3x^2 and g(x)=4-2

 

1. f(g(3))

 

2. g(f(x))2

Answer 1

Hi, Ashley.

 

If you still need some help with this problem, let's see if the following will help to clarify.

 

The two problems that you are facing involve the "composition of functions".  If you are unfamiliar with this, I suggest that you start by rereading the section of your textbook dealing with the composition of functions.  In the meantime, briefly stated, the composition of functions involves substituting one function for the variables of another function.  For the first problem, function g(x) will be substituted for the variable in function f(x).  This can be done in the general case or specifically.  The general case is taking the expression for g(x) and substituting it in f(x) to generate another expression.  The specific case is to substitute a value into g(x) and then to take the resultant value and substitute it into f(x).

 

So, the problem that you may be experiencing is deciding what value of g(x) to substitute into f(x).  As the reply from Danny T. points out, the function g(x) is a constant equal to 2, which has been expressed as the difference of two integers, 4-2. Remember that much of Algebra involves examining and expressing numbers in different ways.  Thus, what then is the value of g(3) given that g(x) is a constant?  Take that value and substitute it into f(x).

 

Once you are comfortable with the behavior of a constant function, the second problem should be quite easy.  Since g(x) is a constant function, does the value of f(x) make a difference?

 

I hope that this will help.

 

Dennis Tharp

 

 

Answer 2

Ans. (1) f(g(3)) = f(2) = 3((2)^2) = 12

 

Ans. (2) g(f(x))2 = 2(2) = 4