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March 27, 2017

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Use composition of functions to show that the functions f(x) = 5x + 7 and
g(x)= 1/5x-7/5 are inverse functions. That is, carefully show that (fog)(x)= x and (gof)(x)= x.

  • Algebra - ,

    g(f(x))=1/5 (5x+7) -7/5
    = x+7/5-7/5=x

    You do the other.

  • Algebra - ,

    f(x)=5x+7
    g(x)=(1/5)x-7/5=(x-7)/5

    (f⁰g)(x)
    = f(g(x))
    = f((x-7)/5)
    = 5((x-7)/5)+7
    = x-7 + 7
    = x

    (g⁰f)(x)
    = g(f(x))
    = g(5x+7)
    = ((5x+7)-7)/5
    = 5x/5
    = x

    I do not know how your book displays the expression, but the first term of
    g(x)= 1/5x-7/5
    offers two possible interpretations, namely (1/5)x or 1/(5x). You might even have been able to solve the problem if it wasn't for the ambiguity.

  • Algebra - ,

    Thank you! I got a ton more of these to do, so you helped greatly! Thanks!

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