Functions
ICSE · Class 12 · Mathematics
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A function f: A → B is defined when:
The number of functions from A to B, where n(A) = 2 and n(B) = 3, is:
The range of f(x) = |x| is:
The range of the signum function f(x) = sgn(x) is:
Sample Questions
The domain of f(x) = √x is:
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[0, ∞)
√x is defined only for x ≥ 0. At x = 0, √0 = 0 is valid. So domain = [0, ∞).
The range of every function is a subset of its co-domain.
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True
By definition, range = f(A) = {f(a): a ∈ A} ⊆ B = co-domain. The range can be a proper subset or equal to the co-domain.
A function f: A → B is onto if:
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Range of f = Co-domain of f
Onto (surjective) means every element of B has at least one pre-image in A, which is equivalent to Range = Co-domain.
A function f: A → B is one-one if:
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f(x₁) = f(x₂) ⟹ x₁ = x₂
One-one (injective) means distinct inputs give distinct outputs. Equivalently: same output implies same input.
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