Let f be a real function given by fx=x-2 Find each of the following: (i) fof (ii) fofof (iii) - Maths -

Question

Let f be a real function given by f x = x - 2
Find each of the following:
(i) fof
(ii) fofof
(iii) (fofof) (38)
(iv) f 2

Also, show that fof ≠ f 2

Global Expert · Accepted Answer

fx=x-2For domain,x-2≥0⇒x≥2Domain of f=[2,∞)Since fis a square-root function, range of f=0,∞So, f:[2,∞)→0,∞i fofRange of f is not a subset of the domain of f
⇒Domainfof=x: x ∈domain of fand fx∈domain of f⇒Domainfof=x: x ∈[2,∞) and x-2∈[2,∞)⇒Domainfof=x: x ∈[2,∞) and x-2≥2⇒Domainfof=x: x ∈[2,∞) and  x-2≥4⇒Domainfof=x: x ∈[2,∞) and  x≥6⇒Domainfof=x: x≥6⇒Domainfof=[6, ∞)fof :[6, ∞)→Rfof x=f f x=f x-2=x-2-2

ii fofof= (fof) ofWe have, f:[2,∞)→0,∞ and fof : [6, ∞)→R⇒Range of f is not a subset of the domain of fof
Then, domainfofof=x: x ∈domain of fand fx∈domain of fof⇒Domainfofof=x: x ∈[2,∞) and x-2∈[6,∞)⇒Domainfofof=x: x ∈[2,∞) and x-2≥6⇒Domainfofof=x: x ∈[2,∞) and  x-2≥36⇒Domainfofof=x: x ∈[2,∞) and  x≥38⇒Domainfofof=x: x≥38⇒Domainfofof=[38, ∞)fof :[38,∞)→RSo, fofof x=fof f x=fof x-2=x-2-2-2

iii We have, fofof x=x-2-2-2So, fofof 38=38-2-2-2=36-2-2=6-2-2=2-2=0

iv We have, fof=x-2-2⇒f2x=fx×fx=x-2×x-2=x-2So, fof ≠ f2

Let f be a real function given by f x = x - 2 . Find each of the following: (i) fof (ii) fofof (iii) (fofof) (38) (iv) f 2 Also, show that fof ≠ f 2 .

Let f be a real function given by $f (x) = \sqrt{x - 2}$ .
Find each of the following:
(i) fof
(ii) fofof
(iii) (fofof) (38)
(iv) f ²

Also, show that fof ≠ f ² .