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Homework Help: Which of the following is/are true?

  1. Jun 5, 2015 #1
    1. The problem statement, all variables and given/known data
    Which of the following statements are true?
    If f(x)=ex, then f(x)⋅f(-x)=1

    If g(x)=1/x, then g (1/x)=x

    If h(x)=√(x+2), then h(2)=±2

    2. Relevant equations

    3. The attempt at a solution
    Only B
  2. jcsd
  3. Jun 5, 2015 #2


    Staff: Mentor

    I agree, but why do you think that A and C are not true?
  4. Jun 5, 2015 #3
    A) doesn't seem to make sense to me... although x is still unknown.
    C)The answer would be 2 not ±2.
  5. Jun 5, 2015 #4


    Staff: Mentor

    But even without having a specific value for x, can't you evaluate f(x) - f(-x), to see whether it comes out to 1? Otherwise your answer is nothing more than a guess.
  6. Jun 5, 2015 #5
    If f(x)=ex, then f(x)⋅f(-x)=1 Not true:
  7. Jun 5, 2015 #6

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    In (A), it looks to me as though you are writing (i): ##f(x) \times f(-x)##, while Mark44 seems to see (ii): ##f(x) - f(-x)##. Which do you mean: (i) or (ii)?
  8. Jun 5, 2015 #7


    Staff: Mentor

    Oops! My mistake! Thanks for pointing out my error, Ray. I misread that dot as a minus sign. f(x) X f(-x) is indeed equal to 1.
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