Questions on Algebra: Functions, Domain, NOT graphing answered by real tutors!

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Question 167698: Let r(x)=x^2-3 and s(x)=x^3-6. Find r(s(-1)).: Let r(x)=x^2-3 and s(x)=x^3-6. Find r(s(-1)).
Answer by jim_thompson5910(9869) About Me  (Show Source):
You can put this solution on YOUR website!
First find s(-1) (the inner function)


s(x)=x^3-6 Start with the second function.


s(-1)=(-1)^3-6 Plug in x=-1.


s(-1)=-1-6 Cube -1 to get -1.


s(-1)=-7 Subtract.



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Since s(-1)=-7, this means that r(s(-1))=r(-7) (just replace s(-1) with -7)

So let's evaluate r(-7)


r(x)=x^2-3 Start with the first function.


r(-7)=(-7)^2-3 Plug in x=-7.


r(-7)=49-3 Square -7 to get 49.


r(-7)=46 Subtract.


Since r(-7)=46, this means that r(s(-1))=46


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Answer:


So the solution is r(s(-1))=46



Note: there is another way to do this which involves substituting s(x) into r(x) and evaluating the composite function at x=-1. However, this method is a bit more complicated.