Here's my problem for today:

**If ***f(x)* = {(2,3),(4,5),(7,2)} **and ***g(x) = *{(2,1),(3,2),(7,4)}**, then determine **(*f*+*g*)(2) **and **(*f*(*g*(7))**.**

I have no clue how to do this. Help please!

ThisGuy
Jun 26, 2015

#1**+10 **

(f + g)(2) = f(2) + g(2) .........notce that f(2) means that we are just asking what "y" value is associated with x in the function "f" when x = 2 ......this is the point (2,3)......so f(2) = 3

Likewise, g(2) = 1

So...... (f + g)(2) = f(2) + g(2) = 3 + 1 = 4

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f(g(7)).....this means that, first, we are putting "7" into "g" an finding the y value associated with that x value.....this is the point (7,4)....so g(7) = 4

So....so far ......f(g(7)) = f(4).....now.......we are putting "4" into "f" and finding the y value associated with that x value.......this is the point (4,5)......so f(4) = 5

To recap......f(g(7) = f(4) = 5

These are known as "composite" functions.....I'll admit they * ARE* a little tough to grasp !!!!

Post some more questions if you get stuck.....!!!

CPhill
Jun 26, 2015

#1**+10 **

Best Answer

(f + g)(2) = f(2) + g(2) .........notce that f(2) means that we are just asking what "y" value is associated with x in the function "f" when x = 2 ......this is the point (2,3)......so f(2) = 3

Likewise, g(2) = 1

So...... (f + g)(2) = f(2) + g(2) = 3 + 1 = 4

--------------------------------------------------------------------------------------------------------------------------

f(g(7)).....this means that, first, we are putting "7" into "g" an finding the y value associated with that x value.....this is the point (7,4)....so g(7) = 4

So....so far ......f(g(7)) = f(4).....now.......we are putting "4" into "f" and finding the y value associated with that x value.......this is the point (4,5)......so f(4) = 5

To recap......f(g(7) = f(4) = 5

These are known as "composite" functions.....I'll admit they * ARE* a little tough to grasp !!!!

Post some more questions if you get stuck.....!!!

CPhill
Jun 26, 2015