Relations and Functions

Let \( A = \{1, 2, 3\} \) and \( B = \{4, 5, 6\} \). Which of the following is a function from \( A \) to \( B \)?

If \( f : \mathbb{R} \to \mathbb{R} \) is defined by \( f(x) = 3x + 2 \), then \( f^{-1}(x) \) is:

Consider the relation \( R \) on set \( A = \{1,2,3\} \) defined by \( R = \{(1,1),(2,2),(3,3),(1,2)\} \). Which property does \( R \) satisfy?

If \( f : A \to B \) and \( g : B \to C \) are functions where \( f \) is onto and \( g \circ f \) is one-one, then which of the following is true?

Let \( f : \mathbb{R} \to \mathbb{R} \) be defined by \( f(x) = x^2 \). Which of the following statements is true?

If \( R \) is an equivalence relation on set \( A \) with \( |A| = 9 \) and each equivalence class has 3 elements, how many equivalence classes are there?

Let \( f : \mathbb{R} \to \mathbb{R} \) be defined by \( f(x) = \frac{2x+3}{x+1} \), \( x \neq -1 \). Find the inverse \( f^{-1}(x) \).

Which of the following relations on \( \mathbb{Z} \) is an equivalence relation?

If \( f : A \to B \) is a function and \( f(A) = B \), then \( f \) is:

Let \( f : \mathbb{R} \to \mathbb{R} \) be defined by \( f(x) = x^3 - 3x + 1 \). Is \( f \) one-one?