Inverse hyperbolic functions

Inverse hyperbolic functions Quiz

Spec 1.2 · Edexcel International A Level Further Maths: Quiz

Studying this course? Keep your progress in one place.

Pick an answer for each. Quizzes never use energy.

5 questions, one answer each

Each answer is checked as you go, with why.

See all 5 questions

  1. 1. The domain of arcosh⁡x\operatorname{arcosh}x is

    • A. all real xx
    • B. ∣x∣<1|x|<1
    • C. x≥1x\ge1
    • D. x>0x>0

  2. 2. Which is the logarithmic form of arsinh⁡x\operatorname{arsinh}x?

    • A. ln⁡(x+x2+1)\ln\left(x+\sqrt{x^2+1}\right)
    • B. ln⁡(x+x2−1)\ln\left(x+\sqrt{x^2-1}\right)
    • C. 12ln⁡1+x1−x\frac12\ln\frac{1+x}{1-x}
    • D. ln⁡(x−x2+1)\ln\left(x-\sqrt{x^2+1}\right)

  3. 3. The exact value of artanh⁡13\operatorname{artanh}\frac13 is

    • A. ln⁡2\ln2
    • B. 12ln⁡3\frac12\ln3
    • C. ln⁡43\ln\frac43
    • D. 12ln⁡2\frac12\ln2

  4. 4. In proving the log form of arsinh⁡x\operatorname{arsinh}x, why is ey=x−x2+1e^y=x-\sqrt{x^2+1} rejected?

    • A. It is complex
    • B. It is negative, since x2+1>x\sqrt{x^2+1}>x, but ey>0e^y>0
    • C. It is larger than xx
    • D. It makes yy negative

  5. 5. Which function has vertical asymptotes x=1x=1 and x=−1x=-1?

    • A. arsinh⁡x\operatorname{arsinh}x
    • B. arcosh⁡x\operatorname{arcosh}x
    • C. artanh⁡x\operatorname{artanh}x
    • D. sech⁡x\operatorname{sech}x

Quiz