Let f: R to R be a function defined as:f(x) = | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) For $f(x)$ to be continuous,it must be continuous at all points,specifically at the transition points $x=1, x=3,$ and $x=5$.At $x=1$: $\lim_{x 	o

Vedclass · Accepted Answer

not continuous for any values of $a$ and $b$.

Vedclass · Answer

(C) For $f(x)$ to be continuous,it must be continuous at all points,specifically at the transition points $x=1, x=3,$ and $x=5$.At $x=1$: $\lim_{x 	o 1^-} f(x) = 5$ and $\lim_{x 	o 1^+} f(x) = a + b$. Thus,$a + b = 5$ (Equation $i$).At $x=3$: $\lim_{x 	o 3^-} f(x) = a + 3b$ and $\lim_{x 	o 3^+} f(x) = b + 15$. Thus,$a + 2b = 15$ (Equation $ii$).At $x=5$: $\lim_{x 	o 5^-} f(x) = b + 25$ and $\lim_{x 	o 5^+} f(x) = 30$. Thus,$b + 25 = 30 \Rightarrow b = 5$.Substituting $b=5$ into Equation $i$: $a + 5 = 5 \Rightarrow a = 0$.Substituting $a=0$ and $b=5$ into Equation $ii$: $0 + 2(5) = 10$,but the right side is $15$. Since $10 
eq 15$,the system is inconsistent.Therefore,$f(x)$ is not continuous for any values of $a$ and $b$.

Let $f: R \to R$ be a function defined as:
$f(x) = \begin{cases} 5, & x \le 1 \\ a + bx, & 1 < x < 3 \\ b + 5x, & 3 \le x < 5 \\ 30, & x \ge 5 \end{cases}$
Then $f$ is:

Similar Questions

If $f(x) = \begin{cases} e^x; & x \le 0 \\ |1 - x|; & x > 0 \end{cases}$,then

Find all the points of discontinuity of the greatest integer function defined by $f(x) = [x]$,where $[x]$ denotes the greatest integer less than or equal to $x$.

The value$(s)$ of $x$ for which the function $f(x) = \begin{cases} 1-x, & x < 1 \\ (1-x)(2-x), & 1 \leq x \leq 2 \\ 3-x, & x > 2 \end{cases}$ fails to be continuous is(are):

The number of points at which the function $f(x) = \frac{\sqrt{11+|x|-6\sqrt{2+|x|}}}{6-2\sqrt{2+|x|}}$ is discontinuous in $(-\infty, \infty)$ is

Examine the continuity of $f$,where $f$ is defined by $f(x) = \begin{cases} \sin x - \cos x, & \text{if } x \neq 0 \\ -1, & \text{if } x = 0 \end{cases}$

Vedclass Test Series

Exam Paper Generator

Online Exam Module

Let $f: R \to R$ be a function defined as:$f(x) = \begin{cases} 5, & x \le 1 \\ a + bx, & 1 < x < 3 \\ b + 5x, & 3 \le x < 5 \\ 30, & x \ge 5 \end{cases}$Then $f$ is: