Question

F(x)=|x-2|+|x|+|x+2|

Answer 1

F (x)=x

Потому что x-2 и x+2 сокращаются

Answer 2

F(x) = -(X-2) + X + (X+2)
f(X) = -X+2 + X + X +2
f(X) = X+4

Answer 3

To understand the function F(x) = |x-2| + |x| + |x+2|, let's break it down into different cases based on the sign of x. The absolute value function |x| is defined as follows:

• For x >= 0, |x| = x
• For x < 0, |x| = -x

Case 1: x >= 2 In this case, all three absolute value expressions are positive since x-2 and x+2 are positive, and x is also positive. Therefore, we can rewrite F(x) as follows:

F(x) = (x - 2) + x + (x + 2) = 3x

Case 2: 0 <= x < 2 In this case, the absolute value of (x - 2) is negative, but the other two are positive. Therefore, we can rewrite F(x) as follows:

F(x) = -(x - 2) + x + (x + 2) = 3x

Case 3: -2 <= x < 0 In this case, the absolute value of (x - 2) and (x) are negative, but the absolute value of (x + 2) is positive. Therefore, we can rewrite F(x) as follows:

F(x) = -(x - 2) - x + (x + 2) = 3

Case 4: x < -2 In this case, all three absolute value expressions are negative. Therefore, we can rewrite F(x) as follows:

F(x) = -(x - 2) - x - (x + 2) = -3x

Putting it all together, the function F(x) is defined as follows:

• For x >= 2, F(x) = 3x
• For 0 <= x < 2, F(x) = 3x
• For -2 <= x < 0, F(x) = 3
• For x < -2, F(x) = -3x

So, the function F(x) has different expressions based on the value of x, but overall it consists of linear segments with different slopes.