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mj1226
29.09.2019 •
Mathematics
If r(x)=2-x^2 and w(x)=x-2, what is the range of (w*r)(x)
a) (-infinity,0]
b) (-infinity,2]
c) [0,infinity)
d) [2,infinity)
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Ответ:
r(x) = 2 - x² and w(x) = x - 2
(w*r)(x) can be obtained by multiplying the both function together
So, (w*r)(x) = w(x) * r(x) = (x-2)*(2-x²)
(w*r)(x) = x (2-x²) - 2(2-x²)
= 2x - x³ - 4 + 2x²
∴ (w*r)(x) = -x³ + 2x² + 2x - 4
It is a polynomial function with a domain equal to R
The range of (w*r)(x) can be obtained by graphing the function
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 (w*r)(x)
As shown in the graph the range of (w*r)(x) is (-∞,∞)
Ответ: