Teaching MPPSC Assistant Professor Mock Test Series 2025 Mathematical Science Analysis Continuity & Differentiability
Let f be a nonconstant polynomial of degree k and let g ∶ \(\mathbb{R}\) → \(\mathbb{R}\) be a bounded continuous function. Which of the following statements is necessarily true?
1
There always exists x0 ∈ \(\mathbb{R}\) such that f(x0) = g(x0)
2
There is no x0 ∈ \(\mathbb{R}\) such that f(x0) = g(x0)
3
There exists x0 ∈ \(\mathbb{R}\) such that f(x0) = g(x0) if k is even
4
There exists x0 ∈ \(\mathbb{R}\) such that f(x0) = g(x0) if k is odd