If f(x) = x^2 - 4, then what is f(f(1))?

[Dillinger4]

Here is the explanation that was given.

"If f(x) = x^2 - 4, then what is f(f(1))?"

To find the answer, first find f(1). Then repeat the process to find

f(f(1)) --> f(1) = 12 - 4 = 1 - 4 = -3 --> f(f(1)) = (-3)2 - 4 = 9 - 4 = 5 --> 4

a) -3
b) 5
c) 8
d) 15
e) 21

I don't understand how to isolate f. It looks like f has to equal somthing then that somthing has to be squared ie. f(1) = f, f * f = f^2.

[riis]

Originally posted by Dilenger4
f(f(1)) --> f(1) = 12 - 4 = 1 - 4 = -3 --> f(f(1)) = (-3)2 - 4 = 9 - 4 = 5 --> 4

5 is the correct answer, but I don't understand why you think it should be 4.

[riis]

BTW, f(f(x)) is nothing more than:
f(f(x)) =
f(x)^2 - 4 =
(x^2 - 4)^2 - 4 =
x^4 - 8x^2 + 16 - 4 =
x^4 - 8x^2 + 12

f(f(1)) is then 1^4 - 8*1^2 + 12 = 1 - 8 + 12 = 5.

[sql_lall]

Originally posted by Dilenger4
9 - 4 = 5 --> 4

I don't understand how to isolate f. It looks like f has to equal somthing then that somthing has to be squared ie. f(1) = f, f * f = f^2.

I think it's time to say d'oh.

Anyway, what do you mean by 'isolate f'??

[SLH]

Originally posted by Dilenger4
I don't understand how to isolate f. It looks like f has to equal somthing then that somthing has to be squared ie. f(1) = f, f * f = f^2.

You don't need to 'isolate' f.

f(x) is just an notation meaning 'a function of f'. F isn't part of that function as such, f( ) is the function.

[Dillinger4]

Posted by riis

5 is the correct answer, but I don't understand why you think it should be 4.

That was what was given to me. I didn't think it was 4.

They said first find f(1). So that is just f. When i look at fx = x^2 - 4 it seem to me that i would have to get f on one side of the equation and f has to equal somthing. Then to get f(f(1)) i just would just square what f equaled. That's at least how my thought process works incorrect at it may be.

[Ecniv]

If f(x) = x^2 - 4, then what is f(f(1))?

f(f(1)) ===> f(-3)

f(1) = 1^2 - 4 = -3
f(-3) = -3^2 -4 = 9 - 4 = 5

Logic


Vince

[Dillinger4]

Ecniv maybe you can explain this for me. The equation is f(x) = x^2 - 4.
Now i notice that you have f(1) = 1^2 - 4 = -3 now why would f(1) be needed? I know we are trying to find f but what happened to the x in f(x) = x^2 - 4? Again you substituted 1 for the x in
f(1) = 1^2 - 4 = -3. x does have a cofficent of one but 1 * x is still x.

Another question. In f(1) = 1^2 - 4 = -3 you end up with -3 which is the value of f. So why do we use this value as a substitution for x?
f(-3) = -3^2 -4 = 9 - 4 = 5

Thanks for the help.

[alkatran]

f(x) = x^2 - 4
f(f(x)) = ?

To make this simple, let's say f(x) = y
So:
f(f(x)) = f(y) = y^2-4

f(y) = y^2-4 = f(x)^2 - 4

f(x)^2-4 = (x^2-4)^2 - 4 = (x^4-8x^2+16)-4 = x^4-8x^2+12
f(f(x)) = f(y) = x^4 - 8x^2 + 12

[beros87]

f(1) is an number
so when you do f(f(1)) it is like when you do f(1) but x is replaced by the answer of f(1) not by 1