If the equation frac{1}{x} + frac{1}{x - 1} + | vedclass

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

Question

(C) Let $f(x) = \frac{1}{x} + \frac{1}{x - 1} + \frac{1}{x - 2}$ and $g(x) = 3x^3$.To find the number of real roots,we analyze the intersection of the

Vedclass · Accepted Answer

$4$

Vedclass · Answer

(C) Let $f(x) = \frac{1}{x} + \frac{1}{x - 1} + \frac{1}{x - 2}$ and $g(x) = 3x^3$.To find the number of real roots,we analyze the intersection of the graphs of $f(x)$ and $g(x)$.The function $f(x)$ has vertical asymptotes at $x = 0$,$x = 1$,and $x = 2$.By plotting the graph of $f(x)$ and the cubic function $g(x) = 3x^3$,we observe the points of intersection.As shown in the graph,the curves intersect at $4$ distinct points.Therefore,the equation has $4$ real roots,so $k = 4$.

If the equation $\frac{1}{x} + \frac{1}{x - 1} + \frac{1}{x - 2} = 3x^3$ has $k$ real roots,then $k$ is equal to -

Similar Questions

The domain of the real-valued function $f(x) = \sqrt{\frac{2-|x|}{3-|x|}}$ is

The range of the real valued function $f(x) = \frac{x^2 + 2x - 15}{2x^2 + 13x + 15}$ is

If the domain of the function $f(x) = \sqrt{\ln(m\sin x + 4)}$ is $R$,then the number of possible integral values of $m$ is:

If $f: R \rightarrow A$ defined by $f(x) = \frac{1}{x^2+2x+2}$,$\forall x \in R$ is surjective,then $A =$

If $f:[-3,2] \rightarrow [0, \sqrt[3]{x}]$ is an onto function defined by $f(n) = \begin{cases} 2+\sqrt[3]{n}, & -3 \leq n \leq -1 \\ n^{2/3}, & -1 < n \leq 2 \end{cases}$, then $x=$

Vedclass Test Series

Exam Paper Generator

Online Exam Module