Four functions are given below. Perform the indicated compositions to determine which functions are inverse to each other. Be sure to simplify the results. f(x) = 7x + 13 g(x) = x/7 - 13 h(x) = x/7 - 13/7 j(x) = 7x + 91 f(g(x)) = -96 g(f(x)) = Conclusion: f and g are not inverses. f(h(x)) = h(f(x)) = Conclusion: f and h ? inverses. j(g(x)) = g(j(x)) = Conclusion: g and j ? inverses.
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Step 1:** Find the composition \(f(g(z))\): Given \(f(z) = 7z + 13\) and \(g(z) = -\frac{z}{7} - 13\), Substitute \(g(z)\) into \(f(z)\): \(f(g(z)) = 7(-\frac{z}{7} - 13) + 13\) \(= -z - 91 + 13\) \(= -z - 78\) ** Show more…
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