Relations and Functions

35 solved questions from Class 12 Mathematics, each with the full working. Tap any question to see the step-by-step solution.

• 1 What is the domain, range, or fundamental theorem introduced in 'Relations and Functions' (Class 12 Mathematics)? medium MCQ Functions & Theorems
• 2 What is the derivative or integral formula associated with 'Relations and Functions'? medium MCQ Calculus & Formulae
• 3 How do you find the solution set or optimum value in 'Relations and Functions'? medium MCQ Problem Solving & Optimization
• 4 How many distinct equivalence relations can be defined on the set S={a,b,c}? hard 4 marks Counting equivalence relations via partitions
• 5 Let f:R→R be defined by f(x)= x^2, x≤ 1 2x+1, x>1 Find the domain and the range of f. medium 2 marks Domain and range of a piecewise function
• 6 Let f:R→R be defined by f(x)=3x-5 and g:R→R by g(x)=(x+2)/3. i Prove that both f and g are one‑one and onto. ii Find the compositions (f° g)(x) and (g° f)(x). iii Determine the inverse function f^-1 and verify that f^-1(f(x))=x for all x∈R. hard 4 marks Composition and inverse of bijective functions
• 7 Consider the relation R from set A={1,2,3,4} to set B={2,4,6,8} given by R={(1,2),(2,4),(3,6),(4,8)}. Which of the following statements is correct? easy MCQ 1 mark Testing a relation for being a function
• 8 Find the inverse function of f(x)=(3x-5)/(2x+1) and state its domain. medium 2 marks Finding inverse of a rational function
• 9 For which real numbers a is the function f(x)=x^2+ax one‑to‑one on mathbb R? Justify your answer. hard 5 marks Injectivity of quadratic functions
• 10 Let f:R → R be defined by f(x)=x^2, x≤ 2 2x-1, x>2 endcases Is f one‑to‑one on R? easy MCQ 1 mark Injectivity of piecewise functions
• 11 Determine the range of f(x)=x^3-6x on the interval [-2,,2]. hard 3 marks Range of a polynomial on a closed interval
• 12 Find the inverse function of f(x)=(5x+2)/(3-x) and state its domain. hard 5 marks Finding inverse of rational function
• 13 Determine whether the function f:R→R defined by f(x)=e^x-3 is one‑to‑one on the whole real line. Justify your answer. easy 2 marks Injectivity of exponential function
• 14 Let f(x)=2x+1 and g(x)=x^2. Find the value of the composition (f° g)(-2).\n\nA) -7\nB) -3\nC) 5\nD) 9 medium MCQ 3 marks Composition of functions
• 15 How many distinct equivalence relations can be defined on the set S={1,2,3,4}? Provide a brief justification. hard 5 marks Equivalence relations and Bell numbers
• 16 How many equivalence relations can be defined on the set S={1,2,3,4,5} that partition S into exactly three equivalence classes? medium 3 marks Counting equivalence relations via set partitions
• 17 Find the inverse function of f(x)=(2x-7)/(5+x) and state its domain and range. hard 4 marks Inverse of a rational function with domain‑range analysis
• 18 Let f:R→R be defined by f(x)=x+1, x≤ 0 2x-3, x>0. Determine whether f is one‑to‑one on R. Justify your answer. medium 2 marks Injectivity of piecewise defined functions
• 19 If f(x)=3x-4 and g(x)=√(x+5) (with domain x≥ -5), find the value of (f° g)(9).\n\nA) 3√14-4\nB) 3√9+4\nC) 3√14+4\nD) 3√5-4 medium MCQ 2 marks Composition of functions
• 20 How many equivalence relations can be defined on the set S={1,2,3,4,5,6} such that the corresponding partition has exactly two equivalence classes, one of size 2 and the other of size 4? medium 2 marks Counting equivalence relations via partitions
• 21 Let f: [2,∞)→ R be defined by f(x)=(x-2)^2. Determine whether f is one‑to‑one on its domain and justify your answer. easy 1 mark One‑to‑one function on restricted domain
• 22 Find the inverse function of h(x)=(4x+1)/(2-x). State the domain and range of h^-1(x). (Give the inverse in the form h^-1(x)=....) hard 4 marks Finding inverse and swapping domain‑range
• 23 Determine whether the function f(x)=x^2-4x+7 is one‑to‑one on mathbb R and justify your answer. medium 3 marks One‑to‑one test via derivative
• 24 Find the inverse function of h(x)=(3x+2)/(,1-2x,) and state its domain and range. hard 5 marks Finding inverse of rational function
• 25 Let f:,[2,∞)→R be defined by f(x)=ln (x-1). Determine whether f is one‑to‑one on its domain and justify your answer. easy 2 marks Monotonicity and injectivity
• 26 Let f(x)=(2x-5)/(,x+3,) and g(x)=x^2+1. Find the value of (gcirc f)(2). medium MCQ 4 marks Function composition
• 27 Determine whether the function f(x)=x^3-3x is one‑to‑one on R and justify your answer. medium 3 marks Injectivity of cubic functions
• 28 Determine whether the function f(x)=x^2-4x+4 is one‑to‑one on the set of real numbers. Justify your answer. easy 1 mark Injectivity of quadratic function
• 29 Let f:R→R be defined by f(x)=x^3, x≥ 0 -x^3, x<0. Find the inverse function f^-1 and state its domain and range. medium 2 marks Inverse of piecewise function
• 30 Find the range of the function f(x)=(x^2-4)/(x-2) for x≠2. hard 3 marks Range of rational function with hole
• 31 Determine whether the function f(x)=x^3-3x is one‑to‑one on the interval [0,2]. Justify your answer. medium 2 marks Injectivity on a closed interval
• 32 Let f(x)=2x+3 and g(x)=x^2-1. Compute (g° f)(4). easy 1 mark Composition of functions
• 33 How many equivalence relations can be defined on the set S{1,2,3,4} such that the partition has exactly two equivalence classes, one of size 2 and the other of size 2? hard 4 marks Counting equivalence relations via partitions
• 34 Let f(x)=5x-2 and g(x)=x^2+1. Find (gcirc f)(3). easy MCQ 2 marks Composition of functions
• 35 For which real numbers a is the function f(x)=x^3+ax one‑to‑one on R? Justify your answer. hard 3 marks Conditions for injectivity of cubic functions