Find the domain of the function f(x) = frac{1 | vedclass

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

Question

(C) For the function $f(x)$ to be defined,the expression inside the square root must be strictly positive:$(x + 1)(e^x - 1)(x - 4)(x + 5)(x - 6) > 0$I

Vedclass · Accepted Answer

$(-5, -1) \cup (0, 4) \cup (6, \infty)$

Vedclass · Answer

(C) For the function $f(x)$ to be defined,the expression inside the square root must be strictly positive:$(x + 1)(e^x - 1)(x - 4)(x + 5)(x - 6) > 0$Identify the critical points by setting each factor to zero:$x + 1 = 0 \implies x = -1$$e^x - 1 = 0 \implies x = 0$$x - 4 = 0 \implies x = 4$$x + 5 = 0 \implies x = -5$$x - 6 = 0 \implies x = 6$The critical points are $\{-5, -1, 0, 4, 6\}$.Arrange these points on the number line in increasing order: $-5, -1, 0, 4, 6$.Using the wavy curve method (sign scheme):For $x > 6$,the expression is positive.For $4 For $0 For $-1 For $-5 For $x Since we require the expression to be strictly greater than zero,the domain is the union of intervals where the expression is positive:$x \in (-5, -1) \cup (0, 4) \cup (6, \infty)$.

Find the domain of the function $f(x) = \frac{1}{\sqrt{(x + 1)(e^x - 1)(x - 4)(x + 5)(x - 6)}}$.

Similar Questions

If $f: R \rightarrow R$ is defined by $f(x) = [\frac{x}{5}]$ for $x \in R$, where $[y]$ denotes the greatest integer not exceeding $y$, then $\{f(x) : |x| < 71\}$ is equal to

Let $f : R \rightarrow R$ be a function defined by $f(x) = \log_{\sqrt{m}}\{\sqrt{2}(\sin x - \cos x) + m - 2\}$,for some $m$,such that the range of $f$ is $[0, 2]$. Then the value of $m$ is $............$

If $[x]$ denotes the greatest integer $\leq x$, then the domain of the function $f(x)=\sqrt{\frac{4-x^2}{[x]+2}}$ is

If $R = \{ (x, y) | x, y \in Z, x^2 + y^2 \le 4 \}$ is a relation in $Z$,then the domain of $R$ is:

For the function $f(x) = \left[ \frac{1}{[x]} \right]$, where $[x]$ denotes the greatest integer less than or equal to $x$, which of the following statements is true?

Vedclass Test Series

Exam Paper Generator

Online Exam Module