Q. 11 D5.0( 1 Vote )

# Let f be a real function given by . Find each of the following:f2Also, show that fof ≠ f2.

We have, f(x) =

Clearly, domain of f = [2, ∞] and range of f = [0, ∞)

We observe that range of f is not a subset of domain of f

Domain of (fof) = {x: x ϵ Domain of f and f(x) ϵ Domain of f}

= {x: x ϵ [2, ∞) and ϵ [2, ∞)}

= {x: x ϵ [2, ∞) and ≥ 2}

= {x: x ϵ [2, ∞) and x – 2 ≥ 4}

= {x: x ϵ [2, ∞) and x ≥ 6}

= [6, ∞)

Now,

(fof)(x) = f(f(x)) = f =

fof: [6, ∞) R defined as

(fof)(x) =

f2(x) = [f(x)]2 = = x – 2

f2: [2, ∞) R defined as

f2(x) = x – 2

fof ≠ f2

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Functions - 0152 mins
Functions - 1047 mins
Functions - 0558 mins
Functions - 0748 mins
Functions - 0947 mins
Battle of Graphs | various functions & their Graphs48 mins
Inverse Trigonometric Functions - 0161 mins
Range of Functions58 mins
Functions - 0253 mins
Functions - 0361 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses