Let f(x) = {4x - 5, x ≤ 2, x - a, x > 2, If lim(x→2) f(x) exists then find the value of a.

Question

Let f(x) = \(\begin{cases} 4\text x-5, \quad \text x\leq2 \\ \text x-a,\quad\text x>2 \end{cases} \)

{4x - 5, x ≤ 2, x - a, x > 2

If \(\lim\limits_{\text x \to0} \) f(x) exists then find the value of a.

Answer 1

f(x) = \(\begin{cases} 4\text x-5, \quad \text x\leq2 \\ \text x-a,\quad\text x>2 \end{cases} \)

{4x - 5, x ≤ 2, x - a, x > 2

Left Hand Limit(L.H.L.):

Right Hand Limit(R.H.L.):