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Statement $-1$ : The equation $x\, log\, x = 2 - x$ is satisfied by at least one value of $x$ lying between $1$ and $2$
Statement $-2$ : 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 $[ 1 , 2]$
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
Solution
$f\left( x \right) = x\log x,f\left( 1 \right) = 0,f\left( 2 \right) = 4$
$g\left( x \right) = 2 – x,g\left( 1 \right) = 1,g\left( 2 \right) = 0$
$\log \,10 > \log \,4 \Rightarrow 1 > \log \,4$
Thus statement- $1$ and $2$ both are true and sataement- $2$ is a correct explanation of statement- $1$.
