To solve the problem, we use the given properties of the function (f(x)):

Step 1: Identify the period of (f(x))

Given (f(x+2) = -f(x)), replace (x) with (x+2):
[f(x+4) = -f(x+2) = -(-f(x)) = f(x)]
Thus, (f(x)) has a period of 4.

Step 2: Simplify (f(7.5)) using periodicity

[f(7.5) = f(7.5 - 4 \times 1) = f(3.5)]

Step 3: Use (f(x+2) = -f(x))

[f(3.5) = f(2 + 1.5) = -f(1.5)]

Step 4: Simplify (f(1.5))

[f(1.5) = f(2 - 0.5) = f(-0.5 + 2) = -f(-0.5)]

Step 5: Apply the odd function property

Since (f(x)) is odd: (f(-0.5) = -f(0.5))
[f(1.5) = -(-f(0.5)) = f(0.5)]

Step 6: Compute (f(0.5))

When (0 \leq x \leq 1), (f(x) = x), so (f(0.5) = 0.5)

[f(3.5) = -f(1.5) = -0.5]

Answer: (\boxed{-\dfrac{1}{2}}) or (\boxed{-0.5})

(\boxed{-0.5}) (or (\boxed{-\dfrac{1}{2}})) is the correct answer.

(\boxed{-0.5})

作者声明:本文包含人工智能生成内容。