Question

The equation x + cosx $=$ a has exactly one positive root. Complete set of values of 'a' is

• A. (0, 1)
• B. $(-\infty ,1)$
• C. (-1,1)
• D. $(1,\infty )$
• E. $(0,\infty )$

Answer 1

Answer: (D)

$(1,\infty )$

Let f(x) = x + cosx a
$\Rightarrow f^{\prime }\left(x\right)=1-sinx\ge 0\forall xϵR.$
Thus f(x) is increasing in $(-\infty ,\infty )$, as zero of f'(x) don't for an interval. f(0) = 1 a
For a positive root, $1-a<0$
$\Rightarrow a>1$