Show that f(x) = 2a + 3b is continuous where a and b are constants

Question

Need help with a question in my book. How do I prove this is continuous. question - Show that f(x) = 2a + 3b is continuous where a and b are constants

Answer 1

The definition you learned is Definition in terms of limits of functions:

If $f(x)=2a+3b=k$ we have $\lim_{h\to0}|f(x)-f(x+h)|=\lim_{h\to0}|k-k|=\lim_{h\to0}0=0$ and done

Answer 2

$f(x+h)=f (x)=2a+3b $. Thus $lim_{h\to 0}\lvert f (x+h)-f (x)\rvert =lim_{h\to 0}\lvert 2a+3b-(2a+3b)\rvert =lim_{h\to 0} \lvert 0 \rvert =0$.