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Mathematics Question on Relations and functions

If f(x)=log⁡10x2f(x) = \sqrt{\log_{10} x^2} . The set of all values of xx for which f(x)f(x) is real , is

A

[−1,1][-1,1]

B

[1,∞][ 1, \infty ]

C

(−∞,−1](- \infty , - 1 ]

D

(−∞,−1]∪[1,∞)(- \infty , - 1 ] \cup [1, \infty)

Answer

(−∞,−1]∪[1,∞)(- \infty , - 1 ] \cup [1, \infty)

Explanation

Solution

f(x)=log⁡10x2f(x)=\sqrt{\log _{10} x^{2}} is real If log⁡10x2≥0\log _{10} x^{2} \geq 0 ⇒x2≥1\Rightarrow x^{2} \geq 1 ⇒x1\Rightarrow x1 ⇒x∈(−∞,−1]∪[1,∞)\Rightarrow x \in(-\infty,-1] \cup[1, \infty)