Square root inside a square root Hi guys I just want to ask how to...

Kaspaueru2

Kaspaueru2

Answered

2021-12-25

Square root inside a square root
Hi guys I just want to ask how to solve this.
The given is:
f(x)=x
then solve for the (ff)(x)
then it becomes.
(ff)(x)=f(f(x))
f(x)=x
Can the expression be simplified?

Answer & Explanation

vicki331g8

vicki331g8

Expert

2021-12-26Added 37 answers

Answer:
x=x12
x=(x12)12=x14=4{x}
Rita Miller

Rita Miller

Expert

2021-12-27Added 28 answers

As we have the unwritten index 2 for the sqare root, we multiply it by the index of the root inside the first root.
x=x2×2=x4
Another example is: x43=x3×4=x12

karton

karton

Expert

2021-12-30Added 439 answers

The nth root of a number a: an=a1/n
The square root of the square root of x is therefore
x=(x)1/2=(x1/2)1/2=x1/4=x4
Since the domain of x is [0,+), this is also the domain of x=x1/4

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