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Question

Mathematics Question on Functions

The domain of the function f(x)=cos⁡−1x[x]f(x)=\frac{{{\cos }^{-1}}x}{[x]} is

A

[−1,0)∪1[-1,0)\cup \\{1\\}

B

[−1,1][-1,1]

C

[−1,1)[-1,1)

D

none of these

Answer

[−1,0)∪1[-1,0)\cup \\{1\\}

Explanation

Solution

∵f(x)=cos⁡−1x[x]\because f(x)=\frac{\cos ^{-1} x}{[x]}
This function is defined if −1≤x≤1-1 \leq x \leq 1
But [x]≠0[x] \neq 0
⇒x∉[0,1)\Rightarrow x \notin[0,1)
∴\therefore Domain of f(x)=[−1,0)∪1f(x)=[-1,0) \cup\\{1\\}