Download App

RELATIONS AND FUNCTIONS — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSRELATIONS AND FUNCTIONS1 Mark
Question
State True or False for the statements. The composition of functions is commutative.
✓

Answer

Let $f(x) = x^2$
and $g(x) = x + 1$
$fog(x) = f(g(x))$
$= f(x + 1)$
$= (x + 1)^2$
$= x^2 + 2x + 1$
$gof(x) $
$= g(f(x))$
$= g(x^2)$
$ = x^2 + 1$
Thus, $\text{fog}(\text{x})\neq\text{gof}(\text{x})$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "True False[1 Marks ]" from RELATIONS AND FUNCTIONS→RELATIONS AND FUNCTIONS — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

State whether the statements are True or False:
Maximum value of the objective function Z = ax + by in a LPP always occurs at only one corner point of the feasible region.
→
Answer the following as true or false.
Two vectors having same magnitude are collinear.
→
Which of the following statements are True or False.
If matrix AB = 0, then A = 0 or B = 0 or both A and B are null matrices.
→
State True or False for the statements of the following Exercise:
$\begin{vmatrix}\text{x}+1&\text{x}+2&\text{x}+\text{a}\\\text{x}+2&\text{x}+3&\text{x}+\text{b}\\\text{x}+3&\text{x}+4&\text{x}+\text{c}\end{vmatrix}=0,$ where a, b, c are in A.P.
→
State True or False for the following: 
The angle between the line $\vec{\text{r}}=(5\hat{\text{i}}-\hat{\text{j}}-4\hat{\text{k}})+\lambda(2\hat{\text{i}}-\hat{\text{j}}-\hat{\text{k}})$ and the plane $\vec{\text{r}}(3\hat{\text{i}}-4\hat{\text{j}}-\hat{\text{k}})+5=0$ is $\sin^{-1}\Big(\frac{5}{2\sqrt{91}}\Big).$
→
State True or False for the statements of the following Exercise: $|A^{-1}| \neq |A|^{-1},$ where $A$ is non$-$singular matrix.
→
Fill in the blanks.
The feasible region for an LPP is always a _________ polygon.
→
State True or False for the statements:
Let P(A) > 0 and P(B) > 0. Then A and B can be both mutually exclusive and independent.
→
State True or False for the statements of the following Exercise:
The maximum value of $\begin{vmatrix}1&1&1\\1&1+\sin\theta&1\\1&1&1+\cos\theta\end{vmatrix}$ is $\frac{1}{2}.$
→
State True or False for the statements of the following Exercise:
If A and B are matrices of order 3 and |A| = 5, |B| = 3, then |3AB| = 27 × 5 × 3 = 405.
→