Write the relation below as a set of ordered pairs and state if it is a function. If it is not a function, explain why.

Mathematics

1 answer:

AleksAgata [21]3 years ago

7 0

This is a linear function. Let diameter (inches) be x, circumference (inches) be y, observe that the value of y/x is always 3.14. For example, 15.7/5=31.4/10=...=3.14. Therefore, this is not only a function (one to one correspondence from x to y), it's also a linear function that can be represented as y=3.14x.

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Find the inverse of the function

lozanna [386]

as you already know, to get the inverse of any expression we start off by doing a quick switcheroo on the variables and then solving for "y", let's do so.

$\stackrel{h(x)}{y}~~ = ~~6\sqrt[3]{2x+5}-1\implies \stackrel{\textit{quick switcheroo}}{x~~ = ~~6\sqrt[3]{2y+5}-1} \\\\\\ x+1=6\sqrt[3]{2y+5}\implies \cfrac{x+1}{6}=\sqrt[3]{2y+5}\implies \left( \cfrac{x+1}{6} \right)^3=\left( \sqrt[3]{2y+5} \right)^3$

$\left( \cfrac{x+1}{6} \right)^3=2y+5\implies \left( \cfrac{x+1}{6} \right)^3-5=2y\implies \cfrac{\left( \frac{x+1}{6} \right)^3-5}{2}=y \\\\\\ \cfrac{\left( \frac{x+1}{6} \right)^3}{2}-\cfrac{5}{2}=y\implies \cfrac{~~ \frac{(x+1)^3}{6^3}~~}{2}-\cfrac{5}{2}=y\implies \cfrac{(x+1)^3}{432}-\cfrac{5}{2}=\stackrel{y}{h^{-1}(x)}$