Expert: Paul Klarreich - 10/12/2005

Question
hello.. i just have some questions regarding functions.
i have this problems but i'm not sure if tyhey are right
(f-g)(x) f(x)=x+6 and g(x)=2x-4

i resoved it
A>>>(x+6)-(2x-4)
    -x +10
b>>>(fg)(x)POSSIBLE ANSWER
(x+6)(2x-4)
2x^2-4x+12x-24
2x^2+8x-24

c>>> domain of (f/g)(x)... =this is where i have most of my problems i'm not sure how to get the domain..

d>>> f(x)=2x+3/x-3 and g(x)=root of x +1
(fog)(x)
POSSIBLE ANSWER

2*x +1 +3/*x-1-3 (times)*x+1
                       *x+1
=2+3/-3 =5/-3
 
*root

AND WHAT IS THE DOMAIN OF (FoG)(X)

i hope you can help me because i'm really confuse

Answer
Hi, Andrea,

You can think of functions in several ways == a black box, a computer program, etc.  But here is a way to think of what you have to do.

Let FRANK be the person who computes f.
Let GEORGE be the person who computes g.
YOU are their coordinator.

If you want f(37), you call Frank and give him the 37, and he calls you back with the answer.  Same with George.

If you want  (f + g)(37), you call both of them, give each the 37, wait for their answers, and then add them.

Same with (f - g)(x), fg(x) -- multiplication, that is, and division:  (f/g)(x), with a small warning about domains.

BUT if you want  (f o g)(x), which is better written as f(g(x)), the routine is different.

To get f(g(37)), you call GEORGE and give him the 37.  When he calls back with the answer, you give THAT ANSWER to FRANK.

Now, then:
===================================

hello.. i just have some questions regarding functions.
i have this problems but i'm not sure if tyhey are right
(f-g)(x) f(x)=x+6 and g(x)=2x-4

If f(x) = x + 6,  and  g(x) = 2x - 4, then

(f - g)(x) means f(x) - g(x) = x + 6 - (2x - 4)

i resoved it
A>>>(x+6)-(2x-4)
   -x +10
=================== Yes, that's right.

b>>>(fg)(x)POSSIBLE ANSWER
f(x)g(x) = (x+6)(2x-4)
        =  2x^2-4x+12x-24
        =  2x^2+8x-24

c>>> domain of (f/g)(x)... =this is where i have most of my problems i'm not sure how to get the domain..

BASIC IDEA OF DOMAIN:

This means the set of values for which you can compute the function (or difference, sum, product, OR QUOTIENT).

For (f/g)(x), which means f(x)/g(x), you must not divide by zero.  So any 'x' which makes g(x) = 0 is NOT in the domain.

Since g(x) = 0  means  2x - 4 = 0, which means x = 2,
the domain is all x except 2.

d>>> f(x)=2x+3/x-3 and g(x)=root of x +1
(fog)(x)
POSSIBLE ANSWER
Assuming you mean  g(x) = sqrt(x+1)
f(g(x)) means f(sqrt(x+1))
[USE A FIXED FONT]
 2(sqrt(x+1)) + 3
= -----------------
  sqrt(x+1) - 3
which is not simplified as you did below.


2*x +1 +3/*x-1-3 (times)*x+1
                 *x+1
=2+3/-3 =5/-3

*root

AND WHAT IS THE DOMAIN OF (FoG)(X)

First, any x NOT in the domain of g won't be in the domain of f(g).  That would mean  x >= -1.

Then, any x that would make the denominator zero is not in the domain.

That would mean  sqrt(x + 1) - 3 = 0
or  sqrt(x + 1) = 3
or       x + 1 = 9
            x = 8

So the domain is the set of intervals  [0,8), (8,inf).