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Let M = { f: ℝ  → ℝ | f is continuous } be the ring of...

Let M = { f: ℝ  → ℝ | f is continuous } be the ring of all continuous functions from the real numbers to the real numbers. Let a be any real number and define the following function:

Φa:M→R

f(x)↦f(a)

This is called the evaluation homomorphism.
1. Describe the kernel of the evaluation homomorphism.
2. Is the kernel of the evaluation homomorphism a prime ideal or a maximal ideal or both or neither?

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