The range of the functionfx - sin -xex - x2 - x- x - -1- - where-x-denotes the greatest integer function is

Find the range of the given expressionGiven, f(x) = sin [xe^{x} + x^2 – x]For, sin function range is 1≤sinθ≤ 1 ∀θ∈ RThe given function is also in the form of si ...

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Standard XII

Mathematics

Global Maxima

The range of ...

Question

The range of the function $f (x) = \sin [x e^{{x}} + x^{2} - x]$ , $x ϵ (- 1, \infty)$ where $[x]$ denotes the greatest integer function is

$Φ$

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$[0, 1]$

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$[- 1, 1]$

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$R$

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Solution

The correct option is C
$[- 1, 1]$

Find the range of the given expression
Given, $f (x) = \sin [x e^{{x}} + x^{2} - x]$
For, $\sin$ function range is
$- 1 \leq \sin θ \leq 1 \forall θ \in R$
The given function is also in the form of $\sin (θ)$
So, the range of $f (x)$ is $[- 1, 1]$ .
Hence, the correct option is $C$ , $[- 1, 1]$ .

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The range of the functionf(x)=sin[xe{x}+x2–x], xϵ(–1,∞)where[x]denotes the greatest integer function is

The correct option is C [−1,1]Find the range of the given expressionGiven, f(x)=sin[xe{x}+x2–x]For, sin function range is-1≤sinθ≤1∀θ∈RThe given function is also in the form of sinθSo, the range of f(x) is [-1,1].Hence, the correct option is C, [−1,1].

The range of the function $f (x) = \sin [x e^{{x}} + x^{2} - x]$ , $x ϵ (- 1, \infty)$ where $[x]$ denotes the greatest integer function is