Find the values of ' a ' in the domain of the definition of the function , f
Text Solution
Verified by Experts(i) (ii); (ii) (iii)
( − 1/2, 0] ∪ [1/2, 1)
Sol. f(a) = 
for domain of f(x) ; 2a 2 – a ≥ 0 ⇒ a(2a – 1) ≥ 0
∴ a ∈ (– ∞ , 0] ∪ 
. Let g(x) ≡ x 2 + (a + 1)x + (a – 1) = 0
(i) D ≥ 0
(a + 1) 2 – 4(a – 1) ≥ 0 ⇒ a ∈ R ...(i)
(ii) –2 < – 
< 1 ⇒ – 2 < – 
< 1
⇒ a ∈ 
....(ii)
(iii) g(– 2) > 0 ⇒ 4 – 2(a + 1) + (a – 1) > 0 ⇒ a < 1
(iv) g(1) > 0 ⇒ 1 + a + 1 + a – 1 > 0 ⇒ a > –1/2
Now (i) ∩ (ii) ∩ (iii) ∩ (iv) we get
──────────────────────────────────────────────────────────────────────────────────────────
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