isi-entrance 2026 Q15

isi-entrance · India · UGA Composite & Inverse Functions Injectivity, Surjectivity, or Bijectivity Classification

Let $\mathbb { R }$ be the set of all real numbers. The function $f : \mathbb { R } \rightarrow \mathbb { R }$ defined by $f ( x ) = x ^ { 3 } - 3 x ^ { 2 } + 6 x - 5$ is
(a) one-to-one, but not onto.
(B) one-to-one and onto.
(C) onto, but not one-to-one.
(D) neither one-to-one nor onto.

Let $\mathbb { R }$ be the set of all real numbers. The function $f : \mathbb { R } \rightarrow \mathbb { R }$ defined by $f ( x ) = x ^ { 3 } - 3 x ^ { 2 } + 6 x - 5$ is\\
(a) one-to-one, but not onto.\\
(B) one-to-one and onto.\\
(C) onto, but not one-to-one.\\
(D) neither one-to-one nor onto.

Paper Questions

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