Let f : D → R, where D is the domain of f. Find the inverse of f, if it exists
(i)f (x) = 1 − 2 − x
(ii)f (x) = 
(iii)f(x) = n (x + 
)
(iv)Let f : [0, 3] → [1, 13] is defined by f(x) = x 2 + x + 1, then find f – 1 (x).
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
(i) f –1 Does not exists
(ii) f –1 : R → R ; f − 1 = 7 + (4 − x 5 ) 1/3
(iii) f –1 : R → R ; f –1 = 
(iv) f –1 (x) = 
Sol. (i) f : D → R
f(x) = 1 – 2 –x ⇒ f ′ (x) = 2 – x n2 > 0 increasing function ⇒ one one function
D : [x ∈ R), Range : (– ∞ , 1) ≠ codomain
∴ function is not bijective ∴ f –1 does not exist
(ii) f(x) = (4 – (x – 7) 3 ) 1/5
f ′ (x) = 
(4 – (x – 7) 3 ) – 4/5 . (– 3 (x – 7) 2 ) ≤ 0 decreasing function ⇒ one one function
⇒ 
D : R Range : R = codomain ⇒ onto function is bijective (invertible)
y = (4 – (x – 7) 3 ) 1/5 ⇒ 4 – y 5 = (x – 7) 3
x = 7 + (4 – y 5 ) 1/3 or f –1 (x) = 7 + (4 – x 5 ) 1/3
(iii) f(x) = n 
D : x ∈ R, Range : R
y = n 
or x = 
⇒ f –1 (x) = 
(iv) f : [0, 3] → [0, 13]
y = f(x) = x 2 + x + 1 ⇒ x = 
⇒ x = 
∴ f –1 (x) = 
as f –1 [1, 13] → [0, 3]
──────────────────────────────────────────────────────────────────────────────────────────
Prepare Smarter with CGP Edu
Get practice questions, solutions, and test series in one place.
Write a Review
Share your experience with this question and solution.
Commentary
Send your comment, doubt, correction, or feedback to admin.
Similar Questions
Explore conceptually related problems