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The range of the function f(x)=(sin(pi|x...

The range of the function `f(x)=(sin(pi|x+1|))/(x^(4)+1)` (where `[.]` is the greatest integer function) is

A

`[0, 1]`

B

`[-1, 1]`

C

`{0}`

D

None of these

Text Solution

AI Generated Solution

The correct Answer is:
To find the range of the function \( f(x) = \frac{\sin(\pi |x+1|)}{x^4 + 1} \), we can follow these steps: ### Step 1: Analyze the numerator The numerator is \( \sin(\pi |x+1|) \). The sine function oscillates between -1 and 1 for any real input. Therefore, the maximum value of \( \sin(\pi |x+1|) \) is 1 and the minimum value is -1.
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