For f: R → R, f(x) = x³, f is:
ANot function
BRandom
CBIJECTION (one-one and onto). f⁻¹(y) = y^(1/3) for all y ∈ R
DMany-one
Answer & Solution
Correct answer: C. BIJECTION (one-one and onto). f⁻¹(y) = y^(1/3) for all y ∈ R
x³: strictly increasing (derivative 3x² ≥ 0). Hence one-one. Range = all R (cube of large x is large; cube of negative is negative). Onto. Bijection. f⁻¹ = cube root.
Related questions
The graph of $f(x) = 1/x$ in $\mathbb{R} - \{0\}$ is:The function $f: \mathbb{R} \to \mathbb{R}, f(x) = x^2$ is:A relation $R$ from $A$ to $B$ qualifies as a function when:If $|A| = 3$ and $|B| = 4$, the number of elements in $A \times B$ is:In a class of $30$, $18$ play cricket, $15$ play football, $8$ play both. The number who pDe Morgan's law gives $(A \cap B)'$ as:For sets $A = \{1, 2, 3, 4\}$ and $B = \{3, 4, 5, 6\}$, $A \cup B$ is:If a set $A$ has $4$ elements, the number of subsets of $A$ is: