Okay, what do you do when you plug in g(x)?
You are substituting all of the x's in f(x) for g(x), right?
so if f(g(x)) = (x+1)^2 and g(x) x^2, what would have x been before you plugged in x^2?
x^(1/2).
why?
if you have x^(1/2) and substitute in the x^2 for x you get:
(x^2)^(1/2). when you have an exponent to an exponent, you multiply the two.
2*(1/2)= 1
x^1 = x
that is how the f(g(x)) was formed.
now we know f(x) = [x^(1/2)+1]^2
so we plug in for f(4) = [4^(1/2)+1]^2
4^(1/2) = 2 so,
f(4) = [2+1]^2
f(4) = 3^2
f(4) = 9.
hope that helps.
You are substituting all of the x's in f(x) for g(x), right?
so if f(g(x)) = (x+1)^2 and g(x) x^2, what would have x been before you plugged in x^2?
x^(1/2).
why?
if you have x^(1/2) and substitute in the x^2 for x you get:
(x^2)^(1/2). when you have an exponent to an exponent, you multiply the two.
2*(1/2)= 1
x^1 = x
that is how the f(g(x)) was formed.
now we know f(x) = [x^(1/2)+1]^2
so we plug in for f(4) = [4^(1/2)+1]^2
4^(1/2) = 2 so,
f(4) = [2+1]^2
f(4) = 3^2
f(4) = 9.
hope that helps.
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The reason why this question is confusing is because the last statement (the "find" statement) its written SOOOO POORLY !!!... here is how it should have been written
if f[g(x)] = (x+1)^2 and
g(x) = x^2,
find f(4)
Is it starting to click? I hope so...
1) How do you get f(4) ? Bascially I am asking you how are you able to stick a 4 in the parenthesis area
Answer: set x = 2 and plug it into the g(x) function.
so... g(2) = 2^2 = 4
2) now take that 4 and plug it into f(x) and you get...
f(4) = (2 + 1) ^ 2 = 9
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