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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)

Respuesta :

Matheng
The given function are
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 (-∞,∞)
Ver imagen Matheng
answer is a on e2020

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