We say an equation \( f(x)=g(x) \) is consistent, if the curves \( ...

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We say an equation \( f(x)=g(x) \) is consistent, if the curves \( y=f(x) \) and \( y=g(x) \) touch or intersect at at least one point. If
\( \mathrm{P} \) the curves \( y=f(x) \) and \( y=g(x) \) do not intersect or touch, then the equation \( f(x)=g(x) \) is said to be inconsistent, i.e. has no solution.
The equation \( \sin x=x^{2}+x+1 \) is
(a) consistent and has infinite number of solutions
(b) consistent and has finite number of solutions
(c) inconsistent
(d) consistent and has unique solution
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