f(x)=x^2 and g(x) =|x| then f+g=?
To find the sum of two functions, f(x) = x^2 and g(x) = |x|, we need to add their respective values at any given input x.
Let's break it down step by step:
1. Start with the function f(x) = x^2.
2. Next, consider the function g(x) = |x|. The absolute value function (|x|) returns the positive value of x, regardless of its sign. For positive values of x, g(x) = x, and for negative values of x, g(x) = -x.
3. Now, we can find f + g by adding the values of f(x) and g(x) at any given x.
Let's evaluate f + g for both scenarios:
For x ≥ 0:
Since g(x) = x for positive x-values, we have:
f(x) + g(x) = x^2 + x
For x < 0:
Since g(x) = -x for negative x-values, we have:
f(x) + g(x) = x^2 - x
So, f + g depends on the value of x:
- For x ≥ 0, f + g = x^2 + x
- For x < 0, f + g = x^2 - x
Therefore, the sum of functions f(x) = x^2 and g(x) = |x| is given by the piecewise function:
f + g(x) = x^2 + x, for x ≥ 0
f + g(x) = x^2 - x, for x < 0