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# C3 functions watch

1. f(x) R is [3 + k, ∞)

g(x) R is [-2, ∞)

that's what i got so far, i'm stuck on part b) because i'm quite confused about domain of composite functions...what is the domain of gf(x)?
i know i need to make an equation with 3+k but im not sure what it should be equal to
2. (Original post by ihatePE)

f(x) R is [3 + k, ∞)

g(x) R is [-2, ∞)

that's what i got so far, i'm stuck on part b) because i'm quite confused about domain of composite functions...what is the domain of gf(x)?
i know i need to make an equation with 3+k but im not sure what it should be equal to
Firstly, your range of g(x) is incorrect, you should be able to see this if you plot the graph.
3. (Original post by NotNotBatman)
Firstly, your range of g(x) is incorrect, you should be able to see this if you plot the graph.
oops, i've worked it out again and i came to [0, ∞)
4. (Original post by ihatePE)
oops, i've worked it out again and i came to [0, ∞)
What are the coordinates of the minimum point of g(x) = x^2-6? Is this the minimum point when the domain is restricted to x>-2 ?

Remember when finding the range, you have to consider the values that the function g output, that is the y values of the function, not the input ( x values).
5. (Original post by NotNotBatman)
What are the coordinates of the minimum point of g(x) = x^2-6? Is this the minimum point when the domain is restricted to x>-2 ?

Remember when finding the range, you have to consider the values that the function g output, that is the y values of the function, not the input ( x values).
ooooo is it [-6, ∞)?
6. (Original post by ihatePE)
ooooo is it [-6, ∞)?
Yes.

Now part(b), the function gf can be formed if the range of f is contained within (is a subset of) or equal to the domain of g. You've already worked out the range of g as 3+k. Now work out the least k for the range of the function f under the same restricted domain to be contained within the domain of g.
7. (Original post by NotNotBatman)
Yes.

Now part(b), the function gf can be formed if the range of f is contained within (is a subset of) or equal to the domain of g. You've already worked out the range of g as 3+k. Now work out the least k for the range of the function f under the same restricted domain to be contained within the domain of g.
i have 3 + k ≥ -2
therefore k ≥ -5
8. (Original post by ihatePE)
i have 3 + k ≥ -2
therefore k ≥ -5
That should be correct.
9. (Original post by NotNotBatman)
That should be correct.
thanksss, composites r so complicated urghhh

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