f(x)=arctan(3x)

Frequently Asked Questions

• Find the inverse of \(f(x)=\arctan(3x)\)

  

  $$f^{-1}\left(x\right)=\frac{\tan \left(x\right)}{3}$$

• Evaluate the derivative of \(f(x)=\arctan(3x)\)

  

  $$f^{\prime }\left(x\right)=\frac{3}{1+9x^2}$$

• Find the domain of \(f(x)=\arctan(3x)\)

  

  $$x\in \mathbb{R}$$

• $$\text{Find the }x\text{-intercept/zero}$$ of \(f(x)=\arctan(3x)\)

  

  $$x=0$$

• Find the y-intercept of \(f(x)=\arctan(3x)\)

  

  $$f\left(0\right)=0$$

• Find the vertical asymptotes of \(f(x)=\arctan(3x)\)

  

  $$\text{No vertical asymptotes}$$

• Find the horizontal asymptotes of \(f(x)=\arctan(3x)\)

  

  $$\begin{array}{rl}& f\left(x\right)=\frac{\pi }{2}\\ & f\left(x\right)=-\frac{\pi }{2}\end{array}$$

• Find the oblique asymptotes of \(f(x)=\arctan(3x)\)

  

  $$\text{No oblique asymptotes}$$