$f : R \to [- 1, \infty)$ and $f (x) = l n ([| sin 2 x | + | cos 2 x |])$ (where [.] denotes greatest integer function) then which of the following is NOT correct?

(R^{-} \cap R a n g e o f f (x))

is a null set

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f(x) is periodic but fundamental period is not defined.

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f(x) is invertible in

[0, \frac{π}{4}]

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f(x) is into function.

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Solution

The correct option is C f(x) is invertible in $[0, \frac{π}{4}]$
$∵ 1 \leq | sin 2 x | + | cos 2 x | \leq \sqrt{2} S o, [| s i n 2 x | + | c o s 2 x |] = 1 f (x) = l n (1) = 0$
$\Rightarrow$ it is periodic but fundamental period is not defined.
Also, $(R^{-} \cap R a n g e o f f (x))$ is a null set
f(x) is many one and into fucntion.
Hence, f(x) is not invertible.

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Similar questions

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f (x) = l n ([| sin 2 x | + | cos 2 x |])

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[.]

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