Please check this.

f(x)= 1/(x-1)^2 - 5

D= all real numbers, x does not equal to -5

R= all real numbers, y does not equal to 1

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  1. domain is all reals except where the denominator is zero

    So, if you have

    1/(x-1)^2 - 5

    D= all reals except x=1

    Clearly, 1/(x-1)^2 is smallest when x is huge. Then it is close to zero, but always a little bit positive. So,

    R= all reals y > -5

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