Question

Find the domain in which f(x)=x2 + x is increasing function.​

Answer 1

Answer:

open sidebar

Class 11

MATHS

Functions

Find the domain and range of the function f(x) given by f(x)=x−23−x.

check-circle

Text Solution

Solution :

f(x)=x−2x−3

Domain of f(x) will be any real number except 3 as x=3 will make denominator 0.

∴ Domain =x∈R−{3}.

To find range, we need to draw the graph of f(x).

Here, f'(x)=(3−x−x+2)(3−x)2=1(3−x)2

∴f'(x)>0.

It means, graph of f(x) will always be increasing.

Now, we can draw the graph of f(x).

Please refer to the video to see the graph.

From the graph, we can see that f(x) goes from −∞→∞ except −1.

∴ Range of f(x) will be (−∞,−1)∪(−1,∞).

check-circle