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Let f: R rarr R and g: R rarr R be two g...

Let `f: R rarr R` and `g: R rarr R` be two given functions such that `f` is injective and `g` is surjective. Then which of the following is injective?
a. `gof`
b. `fog`
c. `gog`
d. none of these

A

gof

B

fog

C

gog

D

none of these

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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