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Question 1006594: A function p(x) has a value of 5 when x>0 and a value of -5 when x<0.
A function q is defined as q(x) = x^2 - 4.
What is the value of (q(p(3))?
I get the answer:
Step 1. p(3) = 5 when 3>0 and -5 when 3<0.
Step 2. q(5) = 5^2-4 = 21.
But why did I use 5 in step 2, and what does this mean? Could someone put it in words?
Thank you.
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! "A function p(x) has a value of 5 when x>0 and a value of -5 when x<0."
is the same as saying
p(x) = 5 when x > 0
OR
p(x) = -5 when x < 0
it depends on the value of x. If x is positive, then the function is p(x) = 5. OR, if x is negative, then p(x) = -5. It is impossible for p(x) to be both at the same time since x can't be both positive and negative at the same time.
We need to find p(3) first. This is p(x) when x = 3.
x = 3 makes x > 0 true. Ie, 3 is positive
so p(x) = 5 and p(3) = 5
Notice how we don't even bother with p(x) = -5 because x = 3 is NOT negative.
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now we plug that into q(x) like you did and we get
q(5) = 5^2-4 = 21
so q(p(3)) = 21
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