If f(x) = 1, what is x equal to?

Step-by-step explanation:

if f(x) = 1/(x+1)

the f(f(x)) means, wherever you see an "x" in the function.

plug in the function again.

so plug in "1/(x+1)" wherever you see an x

so...

1/(f(x) + 1)  

1/((1/(x+1))+1)

now you're going to need to fix the denominator.  

at the moment... this is what you're denominator looks like.

1/(x+1) + 1

so, combine them. find the LCD

LCD = x + 1

1/(x + 1) + x + 1 / x + 1

x + 2 / x + 1

that's your new denominator.

f(f(x)) = 1 / (x + 2 / x + 1)

because it's 1 / something. all you need to do is get the reciprocal of that "something"

so, what's the reciprocal of x + 2 / x + 1?

x + 1 / x + 2

that's your final answer.

next one.

remember, same deal, everywhere you see an "x" plug in the original function.

f(x) = x/(x+1)

f(f(x)) = f(x) / ( f(x) + 1 )  

= [x / (x + 1) ] / [ (x / (x + 1) ) + 1 ]

so, right now this is your denominator.

(x / x + 1) + 1

combine, find the LCD, LCD = x + 1

x / x + 1  +  x + 1 / x + 1

2x + 1 / x + 1

that's your new denominator.

so plug it in.  

[x / (x + 1) ] / [2x + 1 / x + 1]

this is a little more complicated. but remember, whenever you divide by a fraction, it's the same as multiplying by it's reciprocal

so...

rewrite it like this.

x / (x + 1) * (x + 1) / 2x + 1

the x + 1 cancel out.

and you're left with

x / 2x + 1

hope that helps!

i found two solutions,   n = 2 • ± √3 = ± 3.4641

step-by-step explanation: