Question:

The equation $x log x = 2 - x$ is satisfied by at least one value of $x$ lying between $1$ and $2$. The function $f(x) = x log x$ is an increasing function in $[1,2]$ and $g (x)=2-x$ is a decreasing function in $[1, 2]$ and the graphs represented by these functions intersect at a point in $[1,2]$

Updated On: Apr 28, 2025

Statement-1 is true; Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
Statement-1 is true; Statement-2 is true; Statement-2 is not correct explanation for Statement-1.
Statement-1 is false, Statement-2 is true.
Statement-1 is true, Statement-2 is false.

Hide Solution

Verified By Collegedunia

The Correct Option is A

Solution and Explanation

$f\left(x\right)=x\,log\,x,\,f\left(1\right) = 0,\,f\left(2\right) = 4$
$g\left(x\right) = 2-x,\,g\left(1\right)=1,\,g\left(2\right) = 0$
$log 10 > log\,4 \Rightarrow 1 > log\,4$
Thus statement -1 and 2 both are true and statement-2 is a correct explanation of statement 1.

Was this answer helpful?

Questions Asked in JEE Main exam

View More Questions

Concepts Used:

Increasing and Decreasing Functions

Increasing Function:

On an interval I, a function f(x) is said to be increasing, if for any two numbers x and y in I such that x < y,

⇒ f(x) ≤ f(y)

Decreasing Function:

On an interval I, a function f(x) is said to be decreasing, if for any two numbers x and y in I such that x < y,

⇒ f(x) ≥ f(y)

Strictly Increasing Function:

On an interval I, a function f(x) is said to be strictly increasing, if for any two numbers x and y in I such that x < y,

⇒ f(x) < f(y)

Strictly Decreasing Function:

On an interval I, a function f(x) is said to be strictly decreasing, if for any two numbers x and y in I such that x < y,

⇒ f(x) > f(y)

Graphical Representation of Increasing and Decreasing Functions