Let f, g:R\(\to\)R be defined, respectively by f(x) = x+1, g(x) = 2x-3. Find f+g, f-g and \(\frac fg\).
Solution and Explanation
f, g: R\(\to\)R is defined as f(x) = x+1, g(x) = 2x-3
(f+g)(x) = f(x) + g(x) = (x+1) + (2x-3) = 3x-2
∴ (f+g)(x) = 3x-2
(f-g)(x) = f(x) - g(x) = (x+1) - (2x-3) = x+1-2x+3 = - x+4
∴ (f-g)(x) = -x+4
(\(\frac fg\))(x) = \(\frac {f(x)}{g(x)}\), g(x)≠0,x∈R
(\(\frac fg\))(x) = \(\frac {x+1}{2x-3}\), 2x-3≠0 or 2x≠3
(\(\frac fg\))(x) = \(\frac {x+1}{2x-3}\), x≠\(\frac 32\)
Top Questions on Relations and functions
Let $R$ be a relation defined on the set $\{1,2,3,4\times\{1,2,3,4\}$ by \[ R=\{((a,b),(c,d)) : 2a+3b=3c+4d\} \] Then the number of elements in $R$ is
- JEE Main - 2026
- Mathematics
- Relations and functions
- Consider a set \( S = \{a, b, c, d\} \). Then the number of reflexive as well as symmetric relations from \( S \to S \) is:
- JEE Main - 2026
- Mathematics
- Relations and functions
- Let \( A = \{-2,-1,0,1,2,3,4\} \) and \( R \) be a relation such that \[ R=\{(x,y): 2x+y \le -2,\ x\in A,\ y\in A\}. \] Let
\( l \) = number of elements in \( R \),
\( m \) = minimum number of elements to be added to \( R \) to make it reflexive,
\( n \) = minimum number of elements to be added to \( R \) to make it symmetric. Then \( (l+m+n) \) is:- JEE Main - 2026
- Mathematics
- Relations and functions
Let \(M = \{1, 2, 3, ....., 16\}\), if a relation R defined on set M such that R = \((x, y) : 4y = 5x – 3, x, y (\in) M\). How many elements should be added to R to make it symmetric.
- JEE Main - 2026
- Mathematics
- Relations and functions
- If set $A$ has 3 elements and set $B$ has 4 elements, then the number of injective mappings from $A$ to $B$ is
- IPU CET - 2025
- Mathematics
- Relations and functions
Questions Asked in CBSE Class XI exam
- Balance the following redox reactions by ion-electron method:
(a)MnO4- (aq) + I - (aq) → MnO2(s) + I2(s) (in basic medium)
(b) MnO4- (aq) + SO2(g) → Mn2+(aq) +HSO4- (aq) (in acidic solution)
(c) H2O2(aq)+Fe2+(aq) → Fe3+ (aq) + H2O (l) (in acidic solution)
(d) Cr2O72-+ SO2(g) → Cr3+ (aq) +SO42- (aq) (in acidic solution)- CBSE Class XI
- Oxidation Number
- Write the resonance structures for SO3 , NO2 and NO3-
- CBSE Class XI
- Kossel-Lewis Approach to Chemical Bonding
- At 700 K, equilibrium constant for the reaction:
\(H_2 (g) + I_2 (g) ⇋ 2HI (g)\)
is 54.8. If 0.5 mol L–1 of HI(g) is present at equilibrium at 700 K, what are the concentration of H2(g) and I2(g) assuming that we initially started with HI(g) and allowed it to reach equilibrium at 700 K?- CBSE Class XI
- Law Of Chemical Equilibrium And Equilibrium Constant
- Find the mean deviation about the mean for the data 4, 7, 8, 9, 10, 12, 13, 17.
- CBSE Class XI
- Statistics
Find the mean deviation about the mean for the data 38, 70, 48, 40, 42, 55, 63, 46, 54, 44.
- CBSE Class XI
- Statistics
Concepts Used:
Relations and functions
A relation R from a non-empty set B is a subset of the cartesian product A × B. The subset is derived by describing a relationship between the first element and the second element of the ordered pairs in A × B.
A relation f from a set A to a set B is said to be a function if every element of set A has one and only one image in set B. In other words, no two distinct elements of B have the same pre-image.
Representation of Relation and Function
Relations and functions can be represented in different forms such as arrow representation, algebraic form, set-builder form, graphically, roster form, and tabular form. Define a function f: A = {1, 2, 3} → B = {1, 4, 9} such that f(1) = 1, f(2) = 4, f(3) = 9. Now, represent this function in different forms.
- Set-builder form - {(x, y): f(x) = y2, x ∈ A, y ∈ B}
- Roster form - {(1, 1), (2, 4), (3, 9)}
- Arrow Representation
