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**Unformatted text preview: **conﬁrm10 that the graphs cross
√
at x = ±3 3. We see that the graph of f is below the graph of g (the thicker curve) on
√
√
−∞, −3 3 ∪ 3 3, ∞ . (+) 0 (−) 0 (+)
√
√
33
−3 3
y = f (x) and y = g (x) As a point of interest, if we take a closer look at the graphs of f and g near x = 0 with
the axes oﬀ, we see that despite the fact they both involve cube roots, they exhibit diﬀerent
behavior near x = 0. The graph of f has a sharp turn, or cusp, while g does not.11
10
11 Or at least conﬁrm to several decimal places
Again, we introduced this feature on page 185 as a feature which makes the graph of a function ‘not smooth’. 318 Further Topics in Functions y = f (x) near x = 0 y = g (x) near x = 0 2. To solve 3(2 − x)1/3 ≤ x(2 − x)−2/3 , we gather all the nonzero terms on one side and obtain
3(2 − x)1/3 − x(2 − x)−2/3 ≤ 0. We set r(x) = 3(2 − x)1/3 − x(2 − x)−2/3 . As in number
1, the denominators of the rational exponents are odd, which means there are...

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