There is an addition sign separating the two terms, so cancelling them would not be possible

keep going! I feel the same way sometimes, a snack usually helps

Hi Mirghani, You can simplify the expression, but it will still be a hairy expression. Let's see how it turns out- f(g(x)) = sqrt (x/x+1)^2 - 1 = s...

I would agree with you...a simplified answer would have no radical in the denominator. Though, when I did it I got: (x^2 +1-sqrt(x^2-1))/x^2. Sal d...

Almost. In the video, it's sqrt((x^2/(1+x)^2) - 1), not sqrt((x^2/(1+x)^2) + 1). Therein lies your mistake; sqrt(-1) is an impossible number. Howev...

With practice, you will most likely be able to find composite functions mentally. This may not happen for all problems, but for some, it certainly...

You could if you were looking at a particular value of x. In this example, Sal was simply using the two functions to build a single function. This...

If you are asking can you change f(x)/[1+f(x)] into f(x)/1 + f(x), the answer is no. Why? 1) The denominator has terms. We can't split the fraction...

Generally, it doesn't matter, but some teachers are pretty irritated with roots in the denominator. Personally, in an exam, I'd rationalize it to b...

I was stuck on this too, but I think the reason is that (t-2)^2 = (t-2)(t-2) . Using the distributive property, you get t^2-4t+4.

It doesn't really matter --- they will both give the same answer, so it's up to you to choose what works best/easiest for you with the problem you'...

h(g(x)) = (x+4)^2 - 2(x+4) Basically each "x" in h(x) gets replaced with (x+4), which if g(x). Then, you simplify. 1) FOIL out (x+4)^2: h(g(x)) = x...

Based upon the rules for dividing with fractions: f/g = (1/x) / g = (1/x) * the reciprocal of g We need to work in reverse 1) Factor denominator to...

It comes from (t-2)^2 (t-2)^2 = (t-2)(t-2) = t^2-2t-2t+4 = t^2-4t+4 To square binomials, you need to use FOIL or the pattern for creating a perfect...

I assume you are asking about the first example on the page. The initial problem statement gives you the equations for f(x) and g(x). It then asks...

(f ∘ g)(x) is read "f of g of x", so the ∘ translates to "of". In this case, if you had functions defined, f(x) and g(x), then to get (f ∘ g)(x) yo...

The challenge problem says, "The graphs of the equations y=f(x) and y=g(x) are shown in the grid below." So basically the two graphs is a visual re...

I don't think their aim is to show you the multiple ways you can evaluate the composite function. The first example they basically show what evalua...

Sometimes it's useful to look at a different point of view. Try this site. Then come back and try this video again. http://www.mathsisfun.com/sets/...