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The function $f(x)=\sec[\log(x+\sqrt{1+x^2})]$ is: |
Even Odd Constant None of these |
Even |
$f(x)=\sec(\log(x+\sqrt{1+x^2}))⇒f(-x)=\sec(\log(-x+\sqrt{1+x^2}))$ so $f(-x)=\sec(\log(-x+\sqrt{1+x^2}×\frac{x+\sqrt{1+x^2}}{x+\sqrt{1+x^2}})$ $f(-x)=\sec(\log(\frac{1}{\sqrt{1+x^2}+x})=\sec(-\log(x+\sqrt{1+x^2}))$ $f(-x)=\sec(\log(x+\sqrt{1+x^2}))$ even function |
