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A function composition problem

  1. Mar 25, 2015 #1
    1. The problem statement, all variables and given/known data
    If ## f(x) = sin^2x + sin^2(x+ π/3) + cosxcos(x+ π/3) ## and $$g(5/4)=1$$, then ##(gof)(x)## is equal to?
    Options are
    0
    1
    sinx
    None of these



    2. Relevant equations
    I know gof(x) is g(f(x)) but here g(x) is not given.

    3. The attempt at a solution
    Basically I think we have to put f(x) value in g(x) but here g(x) is not given,
    What's the use of g(5/4) ?
     
  2. jcsd
  3. Mar 26, 2015 #2

    Mark44

    Staff: Mentor

    Use trig sum formulas to simplify ## f(x) = sin^2x + sin^2(x+ π/3) + cosxcos(x+ π/3) ##. If you're careful, you can get this simplfied a great deal.
     
  4. Mar 26, 2015 #3
    By simplifying I got,
    ## 5/4 + \frac{√3}{2}sin2x ##.
     
  5. Mar 26, 2015 #4
    Sorry, carefulness was required as you said.
    Got on simplifying now 5/4, and then the answer is 1.
    Thanks for the motivation of simplifying.
     
  6. Mar 26, 2015 #5

    Mark44

    Staff: Mentor

    Yes, that's what I got as well.
     
  7. Mar 28, 2015 #6

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Since the only g value you were given was "5/4", if this problem had an answer it had to be 5/4! Of course, you needed Mark44's suggestion to show that it had a solution.
     
  8. Mar 28, 2015 #7
    Ya sometimes applying common sense is of great use but I was thinking something else.
     
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