The graph of the real function f(x)= \log _e (x^3+\sqrt{x^6+1}) is symmetric about the:

NIMCET 2023 Question Paper with solutions

Question : 48 of 120

Marks: +1, -0

The graph of the real function

f(x)=

\log _e (x^3+{√{x^6+1}})

is symmetric about the:

Solution:

f(x)=\log (x^3+{√{x^6+1}})

f(-x)\;=\log [(-x)^3+{√{(-x)^6+1}}]

f(-x)\;=\log [{√{x^6+1}}-x^3]

\;=\log [\;{ ({√{x^6+1}}-x^3) ({√{x^6+1}}+x^3) }/{{√{x^6+1}}+x^3}]

\;=\log (\;{1}/{x^3+{√{x^6+1}}})

\;=\log (x^3+{√{x^6+1}}) ^{-1}

\;=-\log (x^3+{√{x^6+1}})

\;=-f(x) \;\text " Odd function "\;

We should know that odd functions are symmetrical about origin.

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