Find the limits. lim_{xrightarrow-2} g(f(x)) f(x)=x+7 g(x)=x^2

nagasenaz 2020-11-14 Answered
Find the limits. limx2g(f(x))
f(x)=x+7g(x)=x2
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Expert Answer

FieniChoonin
Answered 2020-11-15 Author has 102 answers
Given f(x)=x+7 and g(x)=x2 ,
To find limit of g(f(x)) first find the expression for g(f(x)) and then apply limit to the resulting expression.
We can g(f(x)) as follow:
g(f(x))=g(x+7)
g(x+7)=(x+7)2
=x2+2(7)(x)+72
=x2+14x+49
Therefore, g(f(x))=x2+14x+49
We can the limit for the expression g(f(x)) as follows:
limx2g(f(x))=limx2(x2+14x+49)
=(2)2+14(2)+49
=428+49=25
Therefore limx2g(f(x))=25
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