The value of a for which the function f(x) = {[5x-4,if 0<x≤1][4x^2+3ax,if 1<x<2] is continuous at every point of its domain, is A.13/3 B. 1

Question

The value of a for which the function\(f(x) = \begin{cases}5x-4&,\quad \text{if}\,0<x≤1\\ 4x^2+3ax&,\quad\text{if}\,1<x<2\\\end{cases} \)  is continuous at every point of its domain, is

A. \(\frac{13}{3}\)

B. 1 

C. 0 

D. –1

Answer 1

Option : (D)

Formula :-

(i) A function f(x) is said to be continuous at a point x = a of its domain, if
\(\lim\limits_{x \to a}f(x)\) = f(a)
\(\lim\limits_{x \to a^+}f(a+h)\) = \(\lim\limits_{x \to a^-}f(a-h)\) = f(a) 

Given :-

\(f(x) = \begin{cases}5x-4,\quad \text{if}\,0<x≤1\\ 4x^2+3ax,\quad\text{if}\,1<x<2\\\end{cases} \) 

Now at x = 1

Therefore discontinuous at x = 3.