If `f(x)=sqrt(x^(2))`, then f(x) can also be expressed as

Options

A. x
B. `-x`
C. `+-x`
D. `|x|`

Answer

D

Explanation

`sqrt(x^(2))` indicates the need for the positive square root of `x^(2)`. Therefore, `sqrt(x^(2))=x` if `xge0` and `sqrt(x^(2))=-x` if x`lt0`. This is just the definition of absolute value, and so `sqrt(x^(2))=|x|` is the only answer for all values of x.