SOLUTION: Evaluate the piecewise function at the given value of the independent variable. x^2+5/x+3 if x#-3 g(x)={ ,g(-5) x-7 if x=-3

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Question 1086543: Evaluate the piecewise function at the given value of the independent variable.
x^2+5/x+3 if x#-3
g(x)={ ,g(-5)
x-7 if x=-3
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Piecewise function



The piecewise function has two pieces. In other words, two rules which are

Rule1: g%28x%29+=+%28x%5E2%2B5%29%2F%28x%2B3%29 if x%3C%3E-3

Rule2: g%28x%29+=+x-7 if x=-3

The g(x) function depends on the x value. If x is not equal to -3, then we go with Rule1. If x does equal -3, then we go with Rule2.

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g(-5) indicates that the input is x = -5

Because x = -5, which is not -3, this means we go with Rule1 above.

Plug x = -5 into the equation for Rule1.

g%28x%29+=+%28x%5E2%2B5%29%2F%28x%2B3%29

g%28-5%29+=+%28%28-5%29%5E2%2B5%29%2F%28-5%2B3%29 Note how every x is replaced with -5

g%28-5%29+=+%2825%2B5%29%2F%28-5%2B3%29

g%28-5%29+=+%2830%29%2F%28-2%29

g%28-5%29+=+-15

Answer: -15