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mojhsa [17]
3 years ago
13

For the function f(x)= (8-2x)^2, find f^-1. Determine whether f^-1 is a function.

Mathematics
2 answers:
DanielleElmas [232]3 years ago
7 0
No its not a function :) 

<span>to find the inverse function first expand those brackets </span>

<span>you'll get </span>
<span>f(x)= x^2 - 2x^2 - 2x^2 = 4x^2 </span>
<span>f(x)= x^2 - 4x^2 + 4x^2 </span>
<span>f(x)= x^2 or y=x^2 </span>


<span>to find the inverse, swap x and y around. then make y the subject again </span>

<span>y=x^2 </span>
<span>x=y^2 </span>
<span>Root of x=y </span>

<span>now put -1 into x </span>

<span>it wont work because roots cannot have negative numbers </span>
<span>answer is no</span>
KiRa [710]3 years ago
3 0

f­-1(x) = 8±√x/2; f­-1 is not a function, is the answer

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Check the picture below.

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1)

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now, the top of it, as you notice in the picture, is a semicircle, whose radius is the same as the cone's, 3.

\bf \textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=3 \end{cases}\implies V=\cfrac{4\pi (3)^3}{3}\implies V=36\pi \\\\\\ \stackrel{\textit{half of that for a semisphere}}{V=18\pi }\implies V\approx 56.55

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