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![f(x)=4 x^{3} +7 \\ y=4 x^{3} +7 \\ y-7=4 x^{3}\\ \frac{y-7}{4} =x^{3} \\ \sqrt[3]{\frac{y-7}{4} } = x \\ f^{-1}(x)= \sqrt[3]{\frac{x-7}{4} } \\ \\ f^{-1}(5)= \sqrt[3]{\frac{5-7}{4} } \\ \\f^{-1}(5)= \sqrt[3]{\frac{-2}{4} } \\ \\ \\ f(f^{-1}(5)) = 4(\sqrt[3]{\frac{-2}{4} } )^{3} +7](https://tex.z-dn.net/?f=f%28x%29%3D4+x%5E%7B3%7D+%2B7+%5C%5C+y%3D4+x%5E%7B3%7D+%2B7+%5C%5C+y-7%3D4+x%5E%7B3%7D%5C%5C+%5Cfrac%7By-7%7D%7B4%7D+%3Dx%5E%7B3%7D+%5C%5C+++%5Csqrt%5B3%5D%7B%5Cfrac%7By-7%7D%7B4%7D+%7D+%3D+x+%5C%5C+f%5E%7B-1%7D%28x%29%3D++%5Csqrt%5B3%5D%7B%5Cfrac%7Bx-7%7D%7B4%7D+%7D++%5C%5C++%5C%5C++f%5E%7B-1%7D%285%29%3D++%5Csqrt%5B3%5D%7B%5Cfrac%7B5-7%7D%7B4%7D+%7D++%5C%5C++%5C%5Cf%5E%7B-1%7D%285%29%3D++%5Csqrt%5B3%5D%7B%5Cfrac%7B-2%7D%7B4%7D+%7D++%5C%5C++%5C%5C+++%5C%5C+f%28f%5E%7B-1%7D%285%29%29+%3D+4%28%5Csqrt%5B3%5D%7B%5Cfrac%7B-2%7D%7B4%7D+%7D+%29%5E%7B3%7D+%2B7 "f(x)=4 x^{3} +7 \\ y=4 x^{3} +7 \\ y-7=4 x^{3}\\ \frac{y-7}{4} =x^{3} \\ \sqrt[3]{\frac{y-7}{4} } = x \\ f^{-1}(x)= \sqrt[3]{\frac{x-7}{4} } \\ \\ f^{-1}(5)= \sqrt[3]{\frac{5-7}{4} } \\ \\f^{-1}(5)= \sqrt[3]{\frac{-2}{4} } \\ \\ \\ f(f^{-1}(5)) = 4(\sqrt[3]{\frac{-2}{4} } )^{3} +7")
