If r(X)=2-x^2 and w(X)=X-2, what is the range of (w*r)(X)
2 answers:
The given function are
r(x) = 2 - x² and w(x) = x - 2
<span>(w*r)(x) can be obtained by multiplying the both function together
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So, <span>(w*r)(x) = w(x) * r(x) = (x-2)*(2-x²)</span>
<span>(w*r)(x) = x (2-x²) - 2(2-x²)</span>
= 2x - x³ - 4 + 2x²
∴ <span>(w*r)(x) = -x³ + 2x² + 2x - 4
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<span>It is a polynomial function with a domain equal to R
</span>
The range of <span>(w*r)(x) can be obtained by graphing the function
</span>
To graph (w*r)(x), we need to make a table between x and (w*r)(x)
See the attached figure which represents the table and the graph of <span>(w*r)(x)
</span>
As shown in the graph the range of <span>(w*r)(x) is (-∞,∞)
</span>
r(x) = 2 - x² and w(x) = x - 2
<span>(w*r)(x) can be obtained by multiplying the both function together
</span>
So, <span>(w*r)(x) = w(x) * r(x) = (x-2)*(2-x²)</span>
<span>(w*r)(x) = x (2-x²) - 2(2-x²)</span>
= 2x - x³ - 4 + 2x²
∴ <span>(w*r)(x) = -x³ + 2x² + 2x - 4
</span>
<span>It is a polynomial function with a domain equal to R
</span>
The range of <span>(w*r)(x) can be obtained by graphing the function
</span>
To graph (w*r)(x), we need to make a table between x and (w*r)(x)
See the attached figure which represents the table and the graph of <span>(w*r)(x)
</span>
As shown in the graph the range of <span>(w*r)(x) is (-∞,∞)
</span>
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We are told that the children from a football club are put into rows in the sports hall. When put into rows of 9 children there are 2 children left over. When put into rows of 12 children there are 2 children left over.
We will find least number of children in football club by finding LCM of 9 and 12.
Multiples of 9 are: 9, 18, 27, 36, 45, 54, 63,...
Multiples of 12 are: 12, 24, 36, 48, 60, 72, 84,...
We can see that least common multiple of 9 and 12 is 36.
We are told that 2 children left over from putting them into 9 and 12 children per row. To find least number we will add 2 to 36.
Therefore, the least number of children in the football club is 38.