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NCERT Class 12 Maths Chapter 1: Relations And Functions 12 Questions Solved

NCERT Solutions for Class 12 Maths Chapter 1 Relations And Functions — Exercise 1.2

Click any question below for its step-by-step NCERT textbook solution, concept hints, and worked explanation.

Show that f:ℝ*→ℝ*, f(x)=1/x, is one-one and onto, where ℝ*=ℝ∖{0}. Does the conclusion remain true if the domain is ℕ and codomain…

Check injectivity and surjectivity of (i) f:ℕ→ℕ, f(x)=x²; (ii) f:ℤ→ℤ, f(x)=x²; (iii) f:ℝ→ℝ, f(x)=x²; (iv) f:ℕ→ℕ, f(x)=x³; (v) f:ℤ→ℤ…

Prove that f:ℝ→ℝ, f(x)=⌊x⌋, is neither one-one nor onto.

Prove that f:ℝ→ℝ, f(x)=|x|, is neither one-one nor onto.

Prove that the signum function f:ℝ→ℝ, with f(x)=1 for x>0, f(0)=0 and f(x)=−1 for x<0, is neither one-one nor onto.

Let A={1,2,3}, B={4,5,6,7}, and f={(1,4),(2,5),(3,6)}. Show that f:A→B is one-one.

Classify (i) f:ℝ→ℝ, f(x)=3−4x; (ii) f:ℝ→ℝ, f(x)=1+x², as one-one, onto or bijective, with justification.

For sets A,B, prove that f:A×B→B×A, f(a,b)=(b,a), is bijective.

For ℕ={1,2,…}, define f(n)=(n+1)/2 when n is odd and f(n)=n/2 when n is even. Is f:ℕ→ℕ bijective?

Let A=ℝ∖{3}, B=ℝ∖{1}, and f:A→B, f(x)=(x−2)/(x−3). Is f one-one and onto? Justify.

For f:ℝ→ℝ, f(x)=x⁴, choose the correct classification.

For f:ℝ→ℝ, f(x)=3x, choose the correct classification.