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Maths Solve the following Question.(1 Marks)

Functions · Maharashtra Board STD 11 Science (MSBSHSE - English Medium). 120 questions.

Questions · Page 3 of 3

Solve the following Question.(1 Marks)

Question 1011 Mark
Find $x$, if $g(x)=0$ where$g(x)=\frac{18-2 x^2}{7}$
Answer
$ g(x)=\frac{18-2 x^2}{7}$
$g(x)=0$
$\frac{18-2 x^2}{7}=0$
$\therefore 18-2 x^2=0$
$\therefore x^2=9$
$\therefore x= \pm 3 $
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Question 1021 Mark
Find $x$, if $g(x)=0$ where
$g(x)=\frac{5 x-6}{7}$
Answer
$ g(x)=\frac{5 x-6}{7}$
$g(x)=0$
$\therefore \frac{5 x-6}{7}=0$
$\therefore x=\frac{6}{5} $
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Question 1031 Mark
If $f(m)=m^2-3 m+1$, find
$\left(\frac{\mathbf{f}(2+h)-f(2)}{h}\right), \mathrm{h} \neq 0$.
Answer
$ \left(\frac{\mathbf{f}(2+h)-f(2)}{h}\right)$
$=\frac{(2+h)^2-3(2+h)+1-\left(2^2-3(2)+1\right)}{h}$
$=\frac{\mathrm{h}^2+\mathrm{h}}{\mathrm{h}}$
$=\mathrm{h}+1$
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Question 1061 Mark
If $f(m)=m^2-3 m+1$, find
$f\left(\frac{1}{2}\right)$
Answer
$ f\left(\frac{1}{2}\right)=\left(\frac{1}{2}\right)^2-3\left(\frac{1}{2}\right)+1$
$=\frac{1}{4}-\frac{3}{2}+1$
$=\frac{1-6+4}{4}$
$=-\frac{1}{4}$
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Question 1091 Mark
Check if the relation given by the equation represents $y$ as function of $x$.

$3 x-6=21$

Answer
$3 x-6=21$
$\therefore \mathrm{x}=9$
$\therefore \mathrm{x}=9$ represents a point on the $\mathrm{X}$-axis.
There is no $y$ involved in the equation.
So the given equation does not represent a function.
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Question 1101 Mark
Check if the relation given by the equation represents $y$ as function of $x$.

$2 y+10=0$

Answer
$2 y+10=0$
$\therefore \mathrm{y}=-5$
$\therefore$ For every value of $\mathrm{x}$, there is a unique value of $\mathrm{y}$.
$\therefore \mathrm{y}$ is a function of $\mathrm{x}$.
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Question 1111 Mark
Check if the relation given by the equation represents $y$ as function of $x$.

$x^2-y=25$

Answer
$x^2-y=25$
$\therefore \mathrm{y}=\mathrm{x}^2-25$
$\therefore$ For every value of $\mathrm{x}$, there is a unique value of $\mathrm{y}$.
$\therefore \mathrm{y}$ is a function of $\mathrm{x}$.
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Question 1121 Mark
Check if the relation given by the equation represents $y$ as function of $x$.

$x+y^2=9$

Answer
$\mathrm{x}+\mathrm{y}^2=9$
$\therefore \mathrm{y}^2=9-\mathrm{x}$
$\therefore \mathrm{y}= \pm \sqrt{9-x}$
$\therefore$ For one value of $\mathrm{x}$, there are two values of $\mathrm{y}$.
$\therefore \mathrm{y}$ is not a function of $\mathrm{x}$.
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Question 1131 Mark
Check if the relation given by the equation represents $y$ as function of $x$.

$2 x+3 y=12$

Answer
$2 x+3 y=12$
$\therefore \mathrm{y}=\frac{12-2 x}{3}$
$\therefore$ For every value of $\mathrm{x}$, there is a unique value of $y$.
$\therefore \mathrm{y}$ is a function of $\mathrm{x}$.
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Question 1141 Mark
Which sets of ordered pairs represent functions from A = {1, 2, 3, 4} to B = {-1, 0, 1, 2, 3}? Justify.

{(1, 1), (2, 1), (3, 1), (4, 1)}

Answer
{(1, 1), (2, 1), (3, 1), (4, 1)} represents a function
Reason: Every element of set A has been assigned a unique image in set B.
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Question 1151 Mark
Which sets of ordered pairs represent functions from A = {1, 2, 3, 4} to B = {-1, 0, 1, 2, 3}? Justify.

{(1, 3), (4, 1), (2, 2)}

Answer
{(1, 3), (4, 1), (2, 2)} does not represent a function.
Reason:
3 ∈ A does not have an image in set B.
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Question 1161 Mark
Which sets of ordered pairs represent functions from A = {1, 2, 3, 4} to B = {-1, 0, 1, 2, 3}? Justify.

{(1, 2), (2, -1), (3, 1), (4, 3)}

Answer
{(1, 2), (2, -1), (3, 1), (4, 3)} represents a function.
Reason: Every element of set A has been assigned a unique image in set B.
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Question 1171 Mark
Which sets of ordered pairs represent functions from A = {1, 2, 3, 4} to B = {-1, 0, 1, 2, 3}? Justify.

{(1, 0), (3, 3), (2, -1), (4, 1), (2, 2)}

Answer
{(1, 0), (3, 3), (2, -1), (4, 1), (2, 2)} does not represent a function.
Reason: (2, -1), (2, 2), show that element 2 ∈ A has been assigned two images -1 and 2 from set B.
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Question 1181 Mark
Check if the following relations are functions :

Image

Answer
No, Reason: Not every element of set A has been assigned an image from set B.
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Question 1191 Mark
Check if the following relations are functions:

Image

Answer
No, Reason: An element of set A has been assigned more than one element from set B.
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Question 1201 Mark
Check if the following relations are functions :

Image

Answer
Yes, Reason: Every element of set A has been assigned a unique element in set B.
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Solve the following Question.(1 Marks) - Page 3 - Maths STD 11 Science Questions - Vidyadip