Define f, g : R → R by f (x) = (x − 2)2 andg(x) =1 if x > 0,0 if x = 0,−1 if x < 0.Calculatelimx→2 g(f (x)) and g limx→2 f (x)

Question

Define f, g : R → R by f (x) = (x − 2)2 andg(x) =1 if x > 0,0 if x = 0,−1 if x < 0.Calculatelimx→2 g(f (x)) and g limx→2 f (x)
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Solution 1

First, let's calculate the limit of f(x) as x approaches 2.

lim(x→2) f(x) = lim(x→2) (x - 2)^2

As x approaches 2, (x - 2)^2 approaches 0. So, lim(x→2) f(x) = 0.

Now, let's calculate g(f(x)) as x approaches 2.

g(f(x)) = g((x - 2)^2)

We know that as x approaches 2, (x - 2)^2 (which is f(x)) appro Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study prob

Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solv

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