Draw the graph of the identity function [latex] f: R \rightarrow R: f(x)=x [/latex] for all [latex] x \in R [/latex].

Here [latex] f(x)=x [/latex] for all [latex] x \in R [/latex]. We may prepare its table as under. On a graph paper, we draw [latex] X^{\prime} O X [/latex] and [latex] Y O Y^{\prime} [/latex] as the [latex] x [/latex]-axis and the [latex] y [/latex]-axis respectively. We take 10 small divisions [latex] =1 [/latex] unit. Now, on this graph paper, we plot the points [latex]A(-2,-2), B(-1,-1), O(0,0), C(1,1), D(2,2) \text { and } E(3,3) \text {. }[/latex] Join these points successively to obtain the straight line [latex] A B O C D E [/latex] as the required graph line, given below.

Question 3.4.1: Draw the graph of the identity function f: R → R : f(x) = x ......

Senior Secondary School Mathematics for Class 11 [1185468]

Draw the graph of the identity function $f: R \rightarrow R: f(x)=x$ for all $x \in R$ .

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Here $f(x)=x$ for all $x \in R$ .

We may prepare its table as under.

On a graph paper, we draw $X^{\prime} O X$ and $Y O Y^{\prime}$ as the $x$ -axis and the $y$ -axis respectively.

We take 10 small divisions $=1$ unit.

Now, on this graph paper, we plot the points

A(-2,-2), B(-1,-1), O(0,0), C(1,1), D(2,2) \text { and } E(3,3) \text {. }

Join these points successively to obtain the straight line $A B O C D E$ as the required graph line, given below.

x	-2	-1	0	1	2	3
f(x) = x	-2	-1	0	1	2	3

Question: 3.5.6

Let f be the exponential function and g be the logarithmic function. Then, find: (i) (f + g)(1) (ii) (fg)(1) (iii) (4f)(1) (iv) (3g)(1) ...

Verified Answer:

Let

f: R \rightarrow R: f(x)=e^{x} [/latex...

Question: 3.5.5

Let f and g be real functions , defined by f(x) = √x + 2 and g(x) = √4 – x². Find (i) (f + g)(x) (ii) (f-g)(x) (iii) (fg)(x) (iv) (ff)(x) (v) (gg)(x) (vi) (f/g)(x). ...

Verified Answer:

Clearly,

f(x)=\sqrt{x+2}

is defin...

Question: 3.5.4

Let f and g be real functions defined by f(x) = √x – 1 and g(x) = √x + 1. Find (i) (f + g)(x) (ii) (f – g)(x) (iii) (fg)(x) (iv) (f/g)(x). ...

Verified Answer:

Clearly,

f(x)=\sqrt{x-1}

is defin...

Question 3.4.1: Draw the graph of the identity function f: R → R : f(x) = x ......

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