SOLUTION: Let r(x)=x^2-3 and s(x)=x^3-6. Find r(s(-1)).

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Question 167698: Let r(x)=x^2-3 and s(x)=x^3-6. Find r(s(-1)).
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
First find s%28-1%29 (the inner function)


s%28x%29=x%5E3-6 Start with the second function.


s%28-1%29=%28-1%29%5E3-6 Plug in x=-1.


s%28-1%29=-1-6 Cube -1 to get -1.


s%28-1%29=-7 Subtract.



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Since s%28-1%29=-7, this means that r%28s%28-1%29%29=r%28-7%29 (just replace s%28-1%29 with -7)

So let's evaluate r%28-7%29


r%28x%29=x%5E2-3 Start with the first function.


r%28-7%29=%28-7%29%5E2-3 Plug in x=-7.


r%28-7%29=49-3 Square -7 to get 49.


r%28-7%29=46 Subtract.


Since r%28-7%29=46, this means that r%28s%28-1%29%29=46


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Answer:


So the solution is r%28s%28-1%29%29=46



Note: there is another way to do this which involves substituting s%28x%29 into r%28x%29 and evaluating the composite function at x=-1. However, this method is a bit more complicated.