Let f1: R → R, f2: [0, ∞) → R, f3: R → R and f4: R → [0, ∞) be defined by f1(x) = |x| if x < 0, ex if x ≥ 0; f2(x) = x2; f3(x) = sin x if x < 0, x if x ≥ 0; f4(x) = f2(f1(x)). List - I List - II (P) f4 is (1) Onto but not one-one (Q) f3 is (2) Neither continuous nor one-one (R) f2 o f1 is (3) Differentiable but not one-one (S) f2 is (4) Continuous and one-one

f1(x) = |x| if x < 0, ex if x ≥ 0
f2(x) = x2
f3(x) = sin x if x < 0, x if x ≥ 0
f4(x) = f2(f1(x))
(P) f4(x) = f2(f1(x)) = (f1(x))2
If x < 0, f4(x) = x2
If x ≥ 0, f4(x) = (ex)2 = e2x
The range of f4 is [0, ∞)
f4 is not one-one because f4(-1) = f4(1) = 1
f4 is onto [0, ∞)
Therefore, f4 is onto but not one-one.
(Q) f3(x) = sin x if x < 0, x if x ≥ 0
f3 is neither continuous nor one-one.
(R) f2 o f1(x) = (f1(x))2
If x < 0, f2 o f1(x) = x2
If x ≥ 0, f2 o f1(x) = (ex)2 = e2x
It is differentiable but not one-one.
(S) f2(x) = x2
It is continuous and one-one on [0, ∞)
Therefore, P → 1, Q → 2, R → 3, S → 4
The correct matching is P → 7, Q → 5, R → 8, S → 6