Question

For the equation $1+\sin x=ax$, the number of solutions is

• A. $1$ if $a>1$
• B. at least $3$ if $0<a<1$
• C. $2$ if $a=1$
• D. none of these

Answer 1

Answer: (A)

$1$ if $a>1$

Let take $f\left(x\right)=1-ax+sinx$
$f^{\prime }\left(x\right)=cosx-a$, it will monotonically decreasing if $a>1$
Thus it will intersect only at once to x-axis.