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Let f: RvecRa n dg: RvecR be two given f...

Let `f: RvecRa n dg: RvecR` be two given functions such that `f` is injective and `g` is surjective. Then which of the following is injective? `gof` (b) `fog` (c) `gog` (d) none of these

A

gof

B

fog

C

gog

D

fof

Text Solution

Verified by Experts

The correct Answer is:
D
`f : R rarr R` and `g : R rarr R` such that f is injective and + g is surjective.
Then, g may be one-one or many-one
If g is one-one, then gof is one-one
fog is one-one
gog is one-one
But if g is many-one, then gof is not one-one.
fog is not one-one.
gog is many-one
Now, fof is one-one
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