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siniylev [52]
3 years ago
13

Find all the zeros. SHOW ALL WORK! 5x^3 – 5x = 0 Thank you for your help :)

Mathematics
1 answer:
storchak [24]3 years ago
8 0
Factor
remember
if xy=0, assume that x and y=0
also
difference of 2 perfect squares
a²-b²=(a-b)(a+b)

so
5x³-5x=0
factor out 5x
5x(x²-1)=0
5x(x²-1²)=0
factor perefect square
5x(x-1)(x+1)=0
set each to zero

5x=0
x=0

x-1=0
x=1

x+1=0
x=-1

x=-1 or 0 or 1
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I'm assuming all of (x^2+9) is in the denominator. If that assumption is correct, then,

One possible answer is f(x) = \frac{4}{x},  \ \ g(x) = x^2+9

Another possible answer is f(x) = \frac{4}{x+9}, \ \ g(x) = x^2

There are many ways to do this. The idea is that when we have f( g(x) ), we basically replace every x in f(x) with g(x)

So in the first example above, we would have

f(x) = \frac{4}{x}\\\\f( g(x) ) = \frac{4}{g(x)}\\\\f( g(x) ) = \frac{4}{x^2+9}

In that third step, g(x) was replaced with x^2+9 since g(x) = x^2+9.

Similar steps will happen with the second example as well (when g(x) = x^2)

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Answer:

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▹ Answer

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▹ Step-by-Step Explanation

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