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Question
If f : R → R and g : R → R are defined by f(x) = x5 and g(x) = x4 then check if f, g are one-one and fog is one-one?
Solution
f(x) = x5 – It is one-one function
g(x) = x4 – It is one-one function
fog = fog[g(x)] = f[g(x)]
= f(x4)
= (x4)5
fog = x20
f is one-one, g is not one-one.
∵ g(1) = 14 = 1
g(-1) = (-1)4 = 1
Different elements have same images
fog is not one-one. [∵ fog (1) = fog (-1) = 1]
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