alleryInverse 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}.
Keep practising Unit 1A2: Trigonometric Functions & Inverse Trig
Browse all Unit 1A2: Trigonometric Functions & Inverse Trig questions for AP Calculus AB, or explore more Mathematics topics.
Related questions
In a right triangle, for an acute angle θ, sin θ is defined as:A relation $f$ from $A$ to $B$ is a function if every element of $A$ has:The domain of $f(x)= qrt{4-x^2}$ is:If $(x+1,\,y-2)=(3,\,1)$, then $(x,y)$ equals:The domain of $f(x)= qrt{x-1}$ is:The range of the function $f(x)=x^2,\; x\in\mathbb{R}$ is:The domain of the function $f(x)=\dfrac{1}{x-2}$ is:The reciprocal of sin θ is: