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# Determine where f is continuous:

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Determine where f is continuous:

1. f(x) = sin-1 (2x)

2. f(x) = (sqrt(arctanx)) / (x^2 - 9)

I used a graphing calculator for #1 and found the interval to be [-0.5, 0.5], but is there any way I can do this more algebraically without the use of my graphing calculator?

I don't know how to approach #2 at all...

Thanks so much!

Jun 10, 2022

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Determine where f is continuous:

Hello Guest!

1. f(x) = sin-1 (2x)$$f(x)=sin^{-1}(2x)$$

f(x) is continuous if:   $$\color{blue}x\in \mathbb R\ |\ x\notin \{n\cdot \pi /2\}.$$

2. $$f(x) = \sqrt{arctan\ x} / (x^2 - 9)$$

$$\sqrt{arctan\ x}/(x^2-9)$$  is continuous if: $$\color{blue}x\in \mathbb R\ |\ 0\le x< \infty\ and\ x\ne 3.$$

!

Jun 10, 2022