Question

Let f(x) = |2x-10| +2, show that f is continuous at x=5

Answer 1

f(x) = |2x-10| +2

f is continuous at x,

if f(x) = |2x-10| +2 -> 2x-10 = 0 -> x_o = 5;

$f(x) = \begin{cases} 2x-12 &\text{if } x \ge 5\\ -2x+8 &\text{if } x < 5 \end{cases}$

lim_{x -> 5-}(-2x+8) = -2,

lim_{x -> 5}(2x-12) = -2,

lim_{x -> 5+}(2x-12) = -2 .

It is clearly that the limit of the function at 5-, 5, 5+ is equal to -2.

So the f(x) is continuous at point 5.