Question

Let $f$ be a continuous function on the closed interval $[0,1]$. Let $f(0)=1$ and $f(1)=0$. Which of the following statement is not necessarily true?

• A. There exists a number $k$ in $[0,1]$ such that $f(k)\ge f(x)$ for all $x$ in $[0,1]$
• B. For all $a$ and $b$ in $[0,1]$, if $a=b$, then $f(a)=f(b)$
• C. There exists a number $k$ in $[0,1]$ such that $f(k)=\frac{1}{2}$
• D. There exists a number $k$ in $[0,1]$ such that $f(k)=\frac{3}{2}$

Answer 1

Answer: (D)

Read the statement
recall the properties of continuous functions.