List of top Mathematics Questions on Functions asked in Bihar Board XII

If the operation 'o' is defined as \( (a \, o \, b) = a^3 + b^3 \), then what is \( 4 \, o \, (1 \, o \, 2) \)?

If \( n(A) = 4 \) and \( n(B) = 2 \), then \( n(A \times B) \) is?

If \( f : A \to B \) is an onto function, then

If \( f: \mathbb{R} \to \mathbb{R} \) such that \( f(x) = 3x - 4 \), then which of the following is \( f^{-1}(x) \)?

If operation 'o' is defined as \( (a \, o \, b) = a^2 + b^2 - ab \), then \( (1 \, o \, 2) \, o \, 3 \) is?

Let \( A = \{ 1, 2, 3, ..., n \} \), how many bijective functions \( f: A \to A \) can be defined?

Find \( f \circ g \) and \( g \circ f \) if \[ f(x) = 8x^3 \quad \text{and} \quad g(x) = x^{1/3}. \]

For a function \( f: A \to B \), the function will be onto if: