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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Age 16 to 18 Challenge Level

Consider the symmetry of the graph. Write the equation in the form

$$x^{1/x}=y^{1/y}$$

and consider the graph of $y=x^{1/x}$ from the question Exponential
Trends.