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

Question

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

A. –1 

B. 0 

C. \(\frac{13}{3}\)

D. 1

Answer 1

Option : (A)

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 : -

\(f(x) = \begin{cases} 5x-4 & ,0 <x≤{1}\\ 4x^2+3bx, &, 1<x<{ 2} \end{cases} \)