Question

hi, i wanna know how to answer graph function problem like this one:

http://i58.tinypic.com/5xpfzk.jpg

thank you!

Answer 1

You figured out f(g(-1)) correctly with an answer of 3. But the other one you calculated wrong. g(f(-1)) gives you g(-3). g(-3) = -2. Not -9. Does that help?

Answer 2

that wasn't my answer, it was the professor's answer :)
may i know how to get the answer for both? thanks

Answer 3

Sorry it took me so long to get back to you. I did this again and again, and my answers are not changing. So look at your graphs, and then look at what you need to find. The first one is f(g(-1)). That means you need to look to g(x) first and find out what the value of y is when x = -1. y = 3 when x = 1. Now take that value, the 3 you got from the first function result and use it in f(x), meaning f(3). What is y in this function when x = 3? Look at your f(x) now. When x = 3, y = 3. That one's right and I get it totally. Let's look at the other one now. That one is asking for the composition of g(f(x)), namely g(f(-1)). Look to f(x). When x = -1 on this graph, what is y? y = -3, right? Now use that -3 in your g(x) function, namely g(-3). Look to your g(x) graph and find what y is when x = -3. I'm seeing that that is -2. Not -9. I don't get your prof's reasoning at all. But I'm only a high school math teacher whose crazy about this stuff (doesn't mean I'm always right!) Check it; I encourage you to find out his/her reasoning for the -9. Do you understand my reasoning?