(20 points) 1. For the function $g: \mathbb{R} \to \mathbb{R}$, $g(x) = x^3$, determine whether the function is one-to-one, and whether it is onto. If the function is not onto determine the range $R(g)$.
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In other words, if g(a) = g(b), then a must equal b. For the function g(c) = x^3, let's assume g(a) = g(b) and see if it implies a = b. g(a) = g(b) a^3 = b^3 To solve this equation, we can take the cube root of both sides: ∛(a^3) = ∛(b^3) a = b Since g(a) = Show more…
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