Question on lim x→2 f(4x^2 − 11) = 8?

[alaa amed]

Homework Statement

Determine whether the statement is true or false.
If f is continuous at 5 and f(5) = 8 and f(4) = 3, then
lim x→2 f(4x^2 − 11) = 8.

2. Homework Equations
lim x->a f(x) = f(a)

The Attempt at a Solution

I think the answer to this question is false because limit of f(4x^2 − 11) has to be approaching 8 but I am not sure if this is the right way ti think about this.[/B]

 

[andrewkirk]

Write $x\mapsto f(4x^2 − 11)$ as the composition of two functions $f$ and $g$, where $g(x)=4x^2-11$.
Is $g$ continuous?
What can we say about the composition of two continuous functions?