1A)Q,R
B)P
C)P
D)Q,R
f:R→R and g:R→R be two functions such that f(g(x)) is a one one function.
then answer the following matrix match type questions:
coloumn 1 coloumn 2
A) then f(x) p) must be one-one
B) then g(x) q)may not be one -one
C) if g(x) is onto then f(x) r)may be many- one
D)if g(X) is into then f(x) s) must be many -one
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3 Answers
1okay for instance lets take
f(x)=x2 ...(not a one-one function)
and g(x)=ex (which is a one-one function)
f(g(x))=e2x (which is again one-one function)
so f(x) may or may not b one-one:)
oops luks like sum1 has deleted the post:D
