Answer to Question #177815 in Real Analysis for Nikhil

Question

The function: f : [-1,3]→R defined by: f(x)= 3x+1/(x^2+4) is uniformly continuous on [-1,3].

True or false with full explanation

Answer 1

The Heine–Cantor theorem states that continuous function on a closed interval is uniformly continuous.

$f(x)=\frac{3x+1}{x^2+4}$ is continuous on interval [-1, 3], so the function is uniformly continuous on this interval