Calculus

Let f(x)=(x/x+3).
Find Domain
Find f^(-1) and its domain
Verify f*f^(-1)=f^(-1)*f=x
Find (f(x+h)-f(x))/h.

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asked by Clarita

  1. I bet you mean
    y = x/(x+3)

    The denominator is 0 when x = -3 so x = -3 is not in our domain. Otherwise the domain is all real numbers.

    Inverse
    x = y/(y+3)
    x y + 3 x = y
    y(x-1) = -3 x
    y = -3x/(x-1)
    domain is all real numbers except x = 1
    f[f^(-1)] = f[-3x/(x-1) ]

    = [-3x/(x-1) ] /{ [-3x/(x-1) ]+3 }

    [-3x/(x-1) ]/{[-3x/(x-1) ]+3(x-1)/(x-1)}

    = -3x/{-3x +3x -3}

    = -3x/-3
    = x
    etc

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    posted by Damon

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