Prove that there is only one homotopy class of continuous functions from $X$ to $D$

Question

Question:

Show that if $X$ is a topological space, and $D$ is the disk in the plane, then there is only one homotopy class of continuous functions from $X$ to $D$.

Answer: Only one case I know that if $f$ is a curve on the $D$ then it is homotopic to the center of the $D$, because the disk is path connected. I don't know how to prove in general and I appreciate any guidance.

Answer 1

For any $f: X \to D$, the homotopy

$$F : X\times I \to D, F(x, t) = tf(x)$$

connects $f$ to the constant map.