What is the solution to this equation?? Please explain steps

Question

Let f(x)=#x^2+7# and g(x)= #(x-3)/x#
Find #(f@g)(-3)#

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Answer 1 · 2018-05-28T04:23:52

11

The #@# notation is to indicate compound functions. Specifically, #f@g(x) = f(g(x))#. To evaluate this, you sub in the value of g(x) into f(x).

#f@g(-3) = f(g(-3)) = f((-3-3)/-3) = f(2) = 2^2 + 7 = 11#

Another method to do this is to evaluate the compound function directly, and substitute in the value of -3.

#f@g(x) = f(g(x)) = f((x-3)/x) = ((x-3)/x)^2 + 7#.

#f@g(-3) = ((-3-3)/-3)^2 + 7 = 11#