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Let g(x) = ((x2+1))/(sqrt(x2+4)).

May 29, 2026Mathematics

ScanSolve AI Answer

Graph of g(x) = (x² + 1)/√(x² + 4)

Key points of g(x) = (x² + 1)/√(x² + 4)
Point	x	y
Minimum	0	0.5

Okay, let's continue with this problem.

Step 1: Analyze the function for symmetry.
Let $g(x) = \frac{\ln(x^2+1)}{\sqrt{x^2+4}}$ .
We check for symmetry by evaluating $g(-x)$ :

g(-x) = \frac{\ln((-x)^2+1)}{\sqrt{(-x)^2+4}} = \frac{\ln(x^2+1)}{\sqrt{x^2+4}} = g(x)

Since $g(-x) = g(x)$ , $g(x)$ is an even function.
Now consider $f(x) = \tan^{-1}(g(x))$ . Since $g(x)$ is even,

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