8.3-8.4 Inverse hyperbolic functions and logarithmic forms Quiz: Pearson Edexcel Further Maths, Unit 8

The 20 questions

1. What is the domain of arcosh x?

   • x >= 1
   • -1 < x < 1
   • x > 0
   • All real x

2. What is the domain of artanh x?

   • x >= 1
   • 0 < x < 1
   • -1 < x < 1
   • All real x

3. What is the range of arsinh x?

   • -1 < y < 1, bounded by the tanh range
   • All real numbers
   • y >= 0 only, so no negative values
   • y >= 1 only, from the minimum of cosh

4. Which logarithmic form equals arsinh x?

   • ln(x + sqrt(x^2 - 1))
   • ln(x + sqrt(x^2 + 1))
   • ln((1 + x)/(1 - x))
   • ln(x - sqrt(x^2 + 1))

5. Which logarithmic form equals artanh x?

   • ln(x + sqrt(x^2 + 1))
   • (1/2) ln((1 + x)/(1 - x))
   • (1/2) ln((x - 1)/(x + 1))
   • ln(x + sqrt(x^2 - 1))

6. What is the derivative of arsinh x?

   • 1/sqrt(x^2 - 1)
   • 1/sqrt(x^2 + 1)
   • x/sqrt(x^2 + 1)
   • 1/(1 - x^2)

7. What is the derivative of artanh x?

   • -1/(1 - x^2)
   • 1/sqrt(x^2 - 1)
   • 1/(1 - x^2)
   • 1/(1 + x^2)

8. Evaluate arcosh(1).

   • ln 2
   • 0
   • It is undefined
   • 1

9. Evaluate arsinh(4/3) in logarithmic form.

   • ln 2
   • ln(4/3)
   • ln(5/3)
   • ln 3

10. Evaluate arcosh(5/4) in logarithmic form.

    • ln(3/4)
    • ln 2
    • ln 3
    • ln(5/4)

11. Evaluate artanh(1/2).

    • ln 3
    • (1/2) ln 2
    • ln(1/2)
    • (1/2) ln 3

12. Find d/dx of arcosh(2x) for x > 1/2.

    • 1/sqrt(4x^2 - 1)
    • 1/sqrt(2x^2 - 1)
    • 2/sqrt(4x^2 + 1)
    • 2/sqrt(4x^2 - 1)

13. Find d/dx of artanh(x^2).

    • 1/(1 - x^4)
    • 2x/(1 + x^4)
    • 2x/(1 - x^4)
    • x^2/(1 - x^4)

14. Solve sinh y = 3/4 for y.

    • y = ln(7/4)
    • y = ln 2
    • y = ln(3/4)
    • y = ln(5/4)

15. Solve arcosh x = ln 3 for x.

    • x = 10/3
    • x = 5/3
    • x = 4/3
    • x = 3

16. Find d/dx of arcosh x at x = 2.

    • 1/sqrt(5)
    • sqrt(3)
    • 1/3
    • 1/sqrt(3)

17. Solve artanh x = ln 3 for x.

    • x = 9/10
    • x = 3/4
    • x = 4/5
    • x = 2/3

18. If y = arsinh x, which equation does y satisfy?

    • y = sinh x
    • sinh y = x
    • tanh y = x
    • cosh y = x

19. What is the logarithmic form of arcosh x?

    • ln(sqrt(x^2 - 1) - x)
    • ln(x + sqrt(x^2 + 1))
    • ln(x + sqrt(x^2 - 1))
    • (1/2) ln((1 + x)/(1 - x))

20. Find d/dx of arsinh(2x).

    • 2/sqrt(2x^2 + 1)
    • 1/sqrt(4x^2 + 1)
    • 4x/sqrt(4x^2 + 1)
    • 2/sqrt(4x^2 + 1)

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