Math Is Fun Forum

Hannibal lecter

Member

Registered: 2016-02-11

Posts: 392

Complete the table

Hi please see this question in the following pic :
I tried a lot to solve it and to complete the table values but it didn't work for me
I know composed function and studied it and know how to calculate functions like f(g(x)) or f(f(x)) .. etc but I stopped in this exercise
I don't know what is my weak point that made me stop from solving and understanding it, the silly thing that I got the solution and still don't understand it!

solution from solution book :

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Wisdom is a tree which grows in the heart and fruits on the tongue

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Complete the table

I'm not sure if you know about odd and even functions.  Here's a link for that:

https://www.mathsisfun.com/algebra/func … -even.html

We are told that f(x) is an even function. 

So you can find out the value of f(positive  x) because it will be the same as f(negative  x).

We know that f(-3) = 0 so f(+3) = 0;   f(-2) = 2 so f(+2) = 2;  f(-1) = 2 so f(+1) = 2

That explains the completion of the f(x) column.

We are told that g(x) is an odd function. 

So you can find out the value of g(positive  x) because it will be minus the value of  g(negative x).

We know that g(-3) = 0 so g(+3) = 0; g(-2) = 2 so g(+2) = -2; g(-1) = 2 so g(+1) = -2

That explains the completion of the g(x) column.

Now to get h(x).  To get h you first have to apply f to the value of x (let's say the result is z)and then apply g to z. Note that z may be on a different row from the x that we started with!

x = -3                  f(-3) = z = 0             g(z) = g(0) = 0

x = -2                  f(-2) = z = 2             g(z) = g(2) = -2

x = -1                  f(-1) = z = 2             g(z) = g(2) = -2

x = 0                   f(0) = z = 0              g(z) = g(0) = 0

x = 1                   f(1) = z = 2              g(z) = g(2) = -2

x = 2                   f(2) = z = 2              g(z) = g(2) = -2

x = 3                   f(3) = z = 0              g(z) = g(0) = 0

Hope that helps.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Hannibal lecter

Member

Registered: 2016-02-11

Posts: 392

Re: Complete the table

I am now completely understand how we get f and g
my problem was I tried to start to solve it row by row not the column f first then column g so sorry
now I remamber and completely understand

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Wisdom is a tree which grows in the heart and fruits on the tongue