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Question 995660: If f(2x+1)=2x^2 -1 and g(x)= 3+ x then (g o f)(7) is?? The answer is 20 but i need to know how yo do it thanks
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! i think i figured it out.
first time for everything and this is the first time i saw one like this.
but i got 20 so i must be doing something right.
i think.
you have 2 functions.
f(2x+1) = 2x^2 - 1
g(x) = 3 + x
you want to find the value of gof(7).
gof(x) is equal to g(f(x)).
so was start with f(x).
but it's not f(x), it's f(2x+1)
in order to make that f(7), we have to find a value of x that makes 2x+1 = 7
that value of x = 3.
you have to replace x with 3 in the function.
f(3) = 2x^2 - 1 becomes f(3) = 18 - 1 = 17
you have f(3) = 17.
now you want to take g(x) = 3 + x and replace x with 17.
you will get g(17) = 3 + 17 which then becomes 20.
scary problem, but the whole idea appeared to be that, in order to get f(7), you needed to find the value of x that made 2x+1 = 7.
that value of x was 3).
so f(7) means you have to replace 2x+1 with 7 and that only happens when x = 3.
so f(2x+1) = 2x^2 - 1 becomes f(3) when 2x+1 = 7.
like i said, i never saw one like this before, but i got the right answer so i'm reasonably satisfied i interpreted it correctly.
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