How To Add Fractions Yahoo Answers

hi, i'm kendall roberg, and today about the composition of functions. here we have two functions: f and g. now, f in terms of x is defined as x divided by 4. g is terms of x is defined as x cubed. now, here we have something that's kind of weird, f(g(x)).

How To Add Fractions Yahoo Answers, this is called the composition of the function f with the function g. so let's call it a composition function. now, to figure out what f(g(x)) is, let's first look at g(x). g(x) is x cubed, so anytime you see g(x), you could instead write x cubed.

so we'll do that...now we have f(x^3). now, you may be familiar with figuring out what f(3) is. for example, if you had to find f(3), this would mean you simply replace the x with any x on this side; you replace the x with a 3 here, you replace the x with a 3 there. so f(3) is 3/4. but unfortunately, we don't have f(3) we have f(x^3). but we're going to do pretty much the same thing. instead of replacing x with a 3, we're going to replace it with an x^3. so we have x^3/4. so now we're finished.

f(g(x)) is x^3/4. let's look at a different function. here we have g(f(x)). we have our same f and g to start with, but this time, we're looking at f(x) first. f(x) is x/4, so we can rewrite this as g(x/4). now we need to look at the g function. every where we see an x, we need to write an x/4. so g(x/4) is (x/4)^3. since x was being cubed here, we must now cube x/4.

x/4 cubed is x cubed over 64. so g(f(x)) is x^3/64. so let's compare g(f(x)), x^3/64, to...f(g(x)), which is x^3/4. they're close, but they're different. good luck.