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

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

Start with the second function.

Plug in .

Cube to get .

Subtract.

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Since , this means that (just replace with -7)

So let's evaluate

Start with the first function.

Plug in .

Square to get .

Subtract.

Since , this means that

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Answer:

So the solution is

Note: there is another way to do this which involves substituting into and evaluating the composite function at . However, this method is a bit more complicated.
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