Home › JEE Main › Mathematics › Sets, Relations and Functions › Inverse image f⁻¹(B) under f: X → Y for B ⊆ Y:
Inverse image f⁻¹(B) under f: X → Y for B ⊆ Y:
ASame as image
B∅
CB
D{x ∈ X : f(x) ∈ B} (preimage of set B)
Answer & Solution
Correct answer: D. {x ∈ X : f(x) ∈ B} (preimage of set B)
f⁻¹(B) = preimage = {x ∈ X : f(x) ∈ B}. Defined even if f is not bijection (returns subset, not single element). E.g., for f(x) = x², f⁻¹({4}) = {-2, 2}.
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: