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# How to find domain/range of this? C3! watch

1. The function f is defined by f: x → cos x, 0≤ x ≤ π,
and the function g is defined by g: x → x + π/2 x≥ 0.

(a) What is the range of f(x)?
(b) What is the domain of fg(x)?
(c) What is the range of fg(x)?

I can do the first one: that will just be -1<or equal to f(x) >or equal to 1

But how do you find domain/range of composite function?

Thanks!
2. (Original post by ViolinGirl)
The function f is defined by f: x → cos x, 0≤ x ≤ π,
and the function g is defined by g: x → x + π/2 x≥ 0.

(a) What is the range of f(x)?
(b) What is the domain of fg(x)?
(c) What is the range of fg(x)?

I can do the first one: that will just be -1<or equal to f(x) >or equal to 1

But how do you find domain/range of composite function?

Thanks!
Work out the function fg(x), sketch it, domain, is the range of the x-axis, range is the range of the y-axis
3. fg(x) = cos (x+π/2)

The range for any cos function would be -1 =< fg(x) =< 1

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