Find gof and fog, if
- f(x)=IxI and g(x)=I5x-2I
- f(x)=8x3 and g(x)=x1/3
- f(x)=IxI and g(x)=I5x-2I
- f(x)=8x3 and g(x)=x1/3
Solution and Explanation
(i)f(x)=IxI and g(x)=I5x-2I
therefore (gof)(x)=g(f(x))=g(IxI)=I5IxI-2I
(fog)(x)=f(g(x))=f(I5x-2I)=II5x-2II=I5x-2I.
(ii)f(x)=8x3 and g(x)=x1/3
therefore (gof)(x)=g(f(x))=g(8x3)=(8x3)1/3=2x
(fog)(x)=f(g(x))=f(x 1/3)=8(x 1/3)3=8x
Top Questions on Relations and Functions
A school is organizing a debate competition with participants as speakers and judges. $ S = \{S_1, S_2, S_3, S_4\} $ where $ S = \{S_1, S_2, S_3, S_4\} $ represents the set of speakers. The judges are represented by the set: $ J = \{J_1, J_2, J_3\} $ where $ J = \{J_1, J_2, J_3\} $ represents the set of judges. Each speaker can be assigned only one judge. Let $ R $ be a relation from set $ S $ to $ J $ defined as: $ R = \{(x, y) : \text{speaker } x \text{ is judged by judge } y, x \in S, y \in J\} $.
- CBSE CLASS XII - 2025
- Mathematics
- Relations and Functions
During the festival season, a mela was organized by the Resident Welfare Association at a park near the society. The main attraction of the mela was a huge swing, which traced the path of a parabola given by the equation:\[ x^2 = y \quad \text{or} \quad f(x) = x^2 \]
- CBSE CLASS XII - 2025
- CBSE Compartment XII - 2025
- Mathematics
- Relations and Functions
- Consider the function \( f : \mathbb{R} \rightarrow \mathbb{R} \), defined as \( f(x) = x^3 \). Assertion (A): \( f(x) \) is a one-one function. Reason (R): \( f(x) \) is a one-one function, if co-domain = range.
- CBSE CLASS XII - 2025
- CBSE Compartment XII - 2025
- Mathematics
- Relations and Functions
- The cost and revenue functions are given as: \[ C(x) = 3x^2 + 5x + 200, \quad R(x) = 50x \] Find the number of items that should be sold to maximize the profit.
- CBSE CLASS XII - 2025
- CBSE Compartment XII - 2025
- Mathematics
- Relations and Functions
- Let \( R \) be a relation defined by the teacher to plan the seating arrangement of students in pairs, where \( R = \{(x, y) : x, y \text{ are Roll Numbers of students such that } y = 3x \} \). List the elements of \( R \). Is the relation \( R \) reflexive, symmetric, and transitive? Justify your answer.
- CBSE CLASS XII - 2025
- Mathematics
- Relations and Functions
Questions Asked in CBSE CLASS XII exam
- Three batteries E1, E2, and E3 of emfs and internal resistances (4 V, 2 \(\Omega\)), (2 V, 4 \(\Omega\)) and (6 V, 2 \(\Omega\)) respectively are connected as shown in the figure. Find the values of the currents passing through batteries E1, E2, and E3.
- CBSE CLASS XII - 2025
- Kirchhoff's Laws
- A beam of light coming from a distant source is refracted by a spherical glass ball (refractive index 1.5) of radius 15 cm. Draw the ray diagram and obtain the position of the final image formed.
- A charge \( -6 \, \mu C \) is placed at the center B of a semicircle of radius 5 cm, as shown in the figure. An equal and opposite charge is placed at point D at a distance of 10 cm from B. A charge \( +5 \, \mu C \) is moved from point C to point A along the circumference. Calculate the work done on the charge.
- CBSE CLASS XII - 2025
- Electrostatics
- If $\tan^{-1} (x^2 - y^2) = a$, where $a$ is a constant, then $\frac{dy}{dx}$ is:
- CBSE CLASS XII - 2025
- Continuity and differentiability
- Kamala Das in ‘Keeping Quiet’ and Keats in ‘A Thing of Beauty’ depict nature as a source of inspiration and strength to man. Analyse both the poems in terms of the above perspective.
- CBSE CLASS XII - 2025
- Literature