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Question
Graph the functions f(x) = x3 and g(x) = `root(3)(x)` on the same coordinate plane. Find f o g and graph it on the plane as well. Explain your results
Solution
Given functions are f(x) = x3 and g(x) = `x^((1/3))`
fog(x) = f(g(x))
= `f(x^(1/3))`
= `(x^(1/3))^3` = x
f(x) = x3
| x | 0 | 1 | – 1 | 2 | – 2 |
| y | 0 | 1 | – 1 | 8 | – 8 |
g(x) = `x^((1/3))`
| x | 0 | 1 | – 1 | 8 | – 8 |
| y | 0 | 1 | – 1 | 2 | – 2 |
Graph of fog(x) = x
| x | 0 | 1 | – 1 | 2 | – 2 | 3 |
| y | 0 | 1 | – 1 | 2 | – 2 | 3 |
Since fog(x) = x is symmetric about the line y = x, g(x) is the inverse image of f(x).
∴ g(x) = f–1(x)
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