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Calculus Level 1

Given that lim ⁡ x → 1 f ( x ) = 2 \displaystyle \lim_{x\to1} f(x) = 2 and lim ⁡ x → 2 f ( x ) = 1 \displaystyle \lim_{x\to2} f(x) = 1 . What is lim ⁡ x → 1 f ( f ( x ) ) \displaystyle \lim_{x\to1} f(f(x)) ?

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Pi Han Goh by Pi Han Goh , 30, Malaysia

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1 solution

Kushal Bose
Aug 14, 2016

if x tends to 1 then f(x) tends to 2

Here in the given limit putting this lim ⁡ f ( x ) → 2 f ( f ( x ) ) \displaystyle \lim_{f(x) \to2} f(f(x))

Consider f ( x ) = z f(x)=z

lim ⁡ z → 2 f ( z ) \displaystyle \lim_{z \to2} f(z) which is equal to 1 1

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