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प्रश्न
Find fog and gof if : f(x) = sin−1 x, g(x) = x2
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उत्तर
f (x) = sin −1 x, g(x) = x2
f : [−1,1]→ `[(-π)/2 ,π/2]` ; g : R → [0, ∞)
Computing fog:
Clearly, the range of g is not a subset of the domain of f.
Domain (fog) = {x: x ∈ domain of g and g (x) ∈ domain of f }
Domain (fog)={ x: x ∈ R and x2 ∈ [−1,1] }
Domain (fog)={ x : x ∈ R and x ∈ [−1,1] }
Domain of (fog)= [−1,1]
fog : [−1,1] → R
(fog) (x) = f (g (x))
= f (x2)
= sin−1 ( x2)
Computing gof:
Clearly, the range of f is a subset of the domain of g.
fog : [−1,1] → R
(gof) (x) = g (f (x))
= g (sin−1 x )
= ( sin−1 x)2
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