Basic Analysis I — Real Analysis · Problem 6.3.1

Sequences of Functions — Jiri Lebl

Mathematics — Real Analysis · composition-continuity-two-variables

Problem

Let

I, J \subset \mathbb{R}

be intervals. Let

F : I \times J \to \mathbb{R}

be a continuous function of two variables and suppose

f : I \to J

be a continuous function. Show that

F\bigl(x, f(x)\bigr)

is a continuous function on

I