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### Number and algebra

### Geometry and measure

### Probability and statistics

### Working mathematically

### Advanced mathematics

### For younger learners

# Ideal Axes

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Age 16 to 18

Challenge Level

- Problem
- Getting Started
- Student Solutions

If you get stuck, try drawing these on a graph using a spreadsheet
program. This should help you investigate some of the shapes of the
more complicated graphs.

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