If . Which of the following are true / False ? I. The domain of f(x) is II. The range of f(x) is III. The graph of f(x) is symmetric about the y-axis. IV. The graph of f(x) never decreases

JEE MainMathematicsModerateFunctions

If $f(x) = 5^{\sqrt{4x^{2} - 1}}$ . Which of the following are
true / False ?
I. The domain of f(x) is $|x| \geq \frac{1}{2}$
II. The range of f(x) is $y \geq 1$
III. The graph of f(x) is symmetric about the y-axis.
IV. The graph of f(x) never decreases

Show answer and solution

y = 5^{\sqrt{4x^{2} - 1}}

(I) Domain

4x^{2} - 1 \geq 0 \Rightarrow |x| \geq \frac{1}{2}

(II)

\because\sqrt{4x^{2} - 1} \geq 0 \Rightarrow 5^{\sqrt{4x^{2} - 1}} \geq 0 \Rightarrow y \geq 1

\therefore

f(x) is an even function

\because

symmetric about y-axis.

Source: Grass-G / M-17 Mathematics Paper 26 Nov Second.docx

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