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# C4 solving composite equation help (why reject the positive x value?)

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1. I'm stuck on the last question c(ii)

I got

Then when I made it equal to 1 I ended up with
x^2 = 16
x = 4, x = -4

Then the mark scheme has rejected x = 4, and made the final answer x = -4.
I can't grasp why it's done this, the domain for f(x) is 1=<x<=16, and g(x) is -4=<x<=-1.
So 4 and -4 are included in the domains together, but for some reason the mark scheme only cares about the g(x) domain, I don't know why it has disregarded the f(x) domain, can anyone help?
2. (Original post by Sayless)

Then the mark scheme has rejected x = 4, and made the final answer x = -4.
I can't grasp why it's done this, the domain for f(x) is 1=<x<=16, and g(x) is -4=<x<=-1.
So 4 and -4 are included in the domains together, but for some reason the mark scheme only cares about the g(x) domain, I don't know why it has disregarded the f(x) domain, can anyone help?
Well, yeah, it's g's domain that matters here.

Because when you say x=4 and x=-4 is the solution to fg(x) = 1, then you're saying that you can put x=-4 into g(x), this gives you g(-4) and you put that into f(x), to give you f(g(-4)) and that's meant to be 1.

So you're saying that you take x=4 and you put it into g(x), to give you g(4) and then do f(g(4)) = 1. Can you see what's wrong here? You're putting x=4 into g(x), but that's not allowed.
3. (Original post by Zacken)
Well, yeah, it's g's domain that matters here.

Because when you say x=4 and x=-4 is the solution to fg(x) = 1, then you're saying that you can put x=4 into g(x), this gives you g(4) and you put that into f(x), to give you f(g(4)) and that's meant to be 1.

So you're saying that you take x=-4 and you put it into g(x), to give you g(-4) and then do f(g(-4)) = 1. Can you see what's wrong here? You're putting x=-4 into g(x), but that's not allowed.
Ah ok so you put the g(x) into the f(x), meaning you only use the domain for g(x), since x = -4 is the only eligible x value to put into g(x). So if it was reveresed and gf(x) you would look at f(x) domain and then put that x value into the gf(x) to solve it, right?
4. (Original post by Sayless)
Ah ok so you put the g(x) into the f(x), meaning you only use the domain for g(x), since x = -4 is the only eligible x value to put into g(x). So if it was reveresed and gf(x) you would look at f(x) domain and then put that x value into the gf(x) to solve it, right?
Correct.

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