Find fog and gof, if
(i)f(x) = e x ; g(x) = n x
(ii) f(x) = |x| ; g(x) = sin x
(iii) f(x) = sin x ; g(x) = x 2
(iv)f(x) = x 2 + 2 ; g(x) = 1 – 
, x ≠ 1
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
(i) fog = x, x > 0 ; gof = x, x ∈ R
(ii) |sin x|, sin |x|
(iii) sin (x 2 ), (sin x) 2
(iv) 
, 
Sol. (i)f(x) = e x and g(x) = n x ⇒ fog(x) = e n x = x, x > 0 ⇒ gof(x) = n e x = x, x ∈ R
(ii)f(x) = |x| and g(x) = sin x ⇒ fog(x) = f(sin x) = |sin x| ⇒ gof (x) = g(|x|) = sin |x|
(iii)f(x) = sin x and g(x) = x 2 ⇒ fog(x) = sin(g(x)) = sin x 2 ⇒ gof(x) = (f 2 (x)) = (sin x) 2
(iv)f(x) = x 2 + 2, g(x) = 
⇒ fog(x) = g 2 (x) + 2 = 
+ 2 = 
gof(x) = 
= 
──────────────────────────────────────────────────────────────────────────────────────────
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