cmi-entrance 2013 QA1

cmi-entrance · India · ugmath 5 marks Composite & Inverse Functions Injectivity, Surjectivity, or Bijectivity Classification

For sets $A$ and $B$, let $f : A \rightarrow B$ and $g : B \rightarrow A$ be functions such that $f ( g ( x ) ) = x$ for each $x$. For each statement below, write whether it is TRUE or FALSE. a) The function $f$ must be one-to-one.
Answer: $\_\_\_\_$ b) The function $f$ must be onto.
Answer: $\_\_\_\_$ c) The function $g$ must be one-to-one.
Answer: $\_\_\_\_$ d) The function $g$ must be onto.
Answer: $\_\_\_\_$

For sets $A$ and $B$, let $f : A \rightarrow B$ and $g : B \rightarrow A$ be functions such that $f ( g ( x ) ) = x$ for each $x$. For each statement below, write whether it is TRUE or FALSE.\\
a) The function $f$ must be one-to-one.

Answer: $\_\_\_\_$\\
b) The function $f$ must be onto.

Answer: $\_\_\_\_$\\
c) The function $g$ must be one-to-one.

Answer: $\_\_\_\_$\\
d) The function $g$ must be onto.

Answer: $\_\_\_\_$

Paper Questions

QA1 QA10 QA2 QA3 QA4 QA5 QA6 QA7 QA8 QA9 QB1 QB2 QB3 QB4 QB5 QB6