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Show without recourse to any calculating aid that: $$7^{1/2} + 7^{1/3} + 7^{1/4} < 7$$ and $$4^{1/2} + 4^{1/3} + 4^{1/4} > 4$$ Sketch the graph of $$f(x) = x^{1/2} + x^{1/3} + x^{1/4} -x$$