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)

Question

22-02-2016
Mathematics

Answered

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)

Verified Answer :

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Matheng Matheng · Answer 1 · 2018-07-02T08:19:05-04:00

The given function are
r(x) = 2 - x² and w(x) = x - 2
(wr)(x) can be obtained by multiplying the both function together

So, (wr)(x) = w(x) r(x) = (x-2)(2-x²)
(wr)(x) = x (2-x²) - 2(2-x²)
= 2x - x³ - 4 + 2x²

∴ (wr)(x) = -x³ + 2x² + 2x - 4

It is a polynomial function with a domain equal to R

The range of (wr)(x) can be obtained by graphing the function

To graph (wr)(x), we need to make a table between x and (wr)(x)

See the attached figure which represents the table and the graph of (wr)(x)

As shown in the graph the range of (w*r)(x) is (-∞,∞)

tishha tishha · Answer 2 · 2019-04-16T01:37:46-04:00

tishha tishha

16-04-2019

answer is a on e2020

Answer Link

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)

Verified Answer :

Related Questions

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)