Let $f: [0,10) \to [0,10] $ be a continuous function then which is correct

Question

Let $f: [0,10) \to [0,10] $ be a continous map then

(a) $f$ need not have any fixed point

(b) $f$ has atleast $10$ fixed point

(c) $f$ has atleast $9$ fixed point

(d) $f$ has atleast one fixed point

Taking counterexample $f(x) = 1$; I can easily eliminate option (b) and (c) but I have no idea about first and last options.

Any hints will be helpful

Thank you!

Answer 1

Take $f(x)=5+x/2$. This will eliminate (d). So…

Answer 2

Let $f(x)=10$ for $x\in [0, 10)$.