Question

Let f:[a,b]->R and g:[a,b]->R be two continuous functions on [a,b]. Show that the set {x in [a,b]:f(x)=g(x)} is closed in R.

Answer 1

we are given both of them are continuous so

Answer 2

hmm..i gtaa think on this

Answer 3

h=f- g is continuous. The set in question is
\[h^{-1}(0)
\]
Since {0} is closed, the inverse image of it is closed.

Answer 4

The inverse image by a continuous function of a closed set is closed.