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Let $$f:R \rightarrow (0, 1)$$ be a continuous function. Then, which of the following function(s) has (have) the value zero at some point in the interval (0, 1)?
$$x^9 - f(x)$$
$$x - \int_{0}^{\frac{\pi}{2}-x}f(t) \cos t dt$$
$$e^x - \int_{0}^{x}f(t) \sin t dt$$
$$f(x) + \int_{0}^{\frac{\pi}{2}}f(t) \sin t dt$$
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