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verify that the given w=50+2.3(h-60) and h=(w+88)/2.3 are inverses by showing that (w*h)(w)=w and that (h*w)(h)=h.

1 Answer

5 votes
From (1) w = 50 +2.3(h-60) we have w = 50 +2.3h - 138 = -88 +2.3h. And h = w/2.3 + 88/2.3. Substituting into the first line, i.e (w*h)*w we have ((-88+2.3h) * (w/2.3 +88/2.3)) = -88w/2.3 -(88)^2/2.3 + wh + 88h. Multiplying by w, we have -88w^2/2.3 -w(88)^2/2.3 +w^2h +88wh On the other hand, (h*w) gives (w/2.3 +88/2.3) * (-88 +2.3h) = -88w/2.3 + wh -(88)^2/2.3 + 88h Multiplying gives -88w^2/2.3 + w^2h - w(88)^2/2.3 + 88wh. So it follows that they are inverse, but there should be a change of sign methink the question is wrong
User Yusuf Ibrahim
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