Answer:
D. f(x) = √(1 + x).
Explanation:
I'm assuming the () stands for f(x) and the root of 1 - and the root of 1+ has "x" at the end of them.
To determine which function is increasing, we need to check whether the function values increase as the input variable increases.
A. f(x) = √x^2 is equal to |x|, which is increasing for x ≥ 0 and decreasing for x < 0. So, f(x) is increasing for x ≥ 0.
B. f(x) = √1 is a constant function, which is neither increasing nor decreasing.
C. f(x) = √(1 - x) is decreasing for x in the domain [0,1], since as x increases in this domain, the square root of 1-x gets smaller. Therefore, f(x) is not an increasing function.
D. f(x) = √(1 + x) is an increasing function, since as x increases, the square root of 1+x also increases.
Therefore, the function that is increasing is D. f(x) = √(1 + x).