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Stitz-Zeager_College_Algebra_e-book

# Definition 62 the inverse of the exponential function

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Unformatted text preview: 4 x + 3 = 0. After squaring √ √ For instance, −2 ≥ 4 x + 3, which has no solution or −2 ≤ 4 x + 3 whose solution is [−3, ∞). Recall, this means we have produced a candidate which doesn’t satisfy the original equation. Do you remember how raising both sides of an equation to an even power could cause this? 6 7 5.3 Other Algebraic Functions 315 √ both sides, we get 2 − 4 x + 3 = 0, whose solution we have found to be x = 13. Since we squared both sides, we double check and ﬁnd g (13) is, in fact, 0. Our sign diagram and graph of g are below. Since the domain of g is [−3, 13], what we have below is not just a portion of the graph of g , but the complete graph. It is always above or on the x-axis, which veriﬁes our sign diagram. (+) −3 13 The complete graph of y = g (x). 3. The radical in h(x) is odd, so our only concern is the denominator. Setting x + 1 = 0 gives x = −1, so our domain is (−∞, −1) ∪ (−1, ∞). To ﬁnd the zeros of h, we set h(x) = 0. To solve 3 x8x = 0, we cube both sides to get x8x = 0. We get 8x = 0, or x = 0. Below is...
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