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Power Up
Age 16 to 18
Challenge Level 
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
$$f(x) = x^{1/2} + x^{1/3} + x^{1/4} -x$$
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