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Question
Let f(x)=[x]and g(x)=|x|, then evaluate the following:
(gof)(−53)−(fog)(−53)
Let f(x)=[x]and g(x)=|x|, then evaluate the following:
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Solution
[−53]
=[−2+13]=−2,∣∣∣−53∣∣∣=53
[53]=[1+23]=1,[53]=53
[−1]=−1,|−1|=1
gof(−53)−fog(−53)
=g[−53]−f∣∣∣−53∣∣∣=g(−2)−f(53) =|−2|−[53]=2−1=1
=[−2+13]=−2,∣∣∣−53∣∣∣=53
[53]=[1+23]=1,[53]=53
[−1]=−1,|−1|=1
gof(−53)−fog(−53)
=g[−53]−f∣∣∣−53∣∣∣=g(−2)−f(53) =|−2|−[53]=2−1=1
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