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[299678]

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if f[g(x)] = (x+1)^2 and
g(x) = x^2,
find f(x) when x = 4

answer is 9 I need ur explanation to support your answer. Thank you

 

[TKDentist]

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.

 

[299678]

Thank you for your input, but still don't get it. I am so frustrating for this kinds of problem.

 

[dentalWorks]

if f[g(x)] = (x+1)^2 and
g(x) = x^2,
find f(x) when x = 4

answer is 9 I need ur explanation to support your answer. Thank you

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