PUC Science 2nd PUC Class 12 - Karnataka Board PUC Question Bank Solutions for Mathematics

Find fog and gof  if : f(x)= x + 1, g (x) = 2x + 3 .

Find fog and gof  if : f(x) = c, c ∈ R, g(x) = sin `x^2`

Find fog and gof  if : f(x) = `x^2` + 2 , g (x) = 1 − `1/ (1-x)`.

Let f(x) = x² + x + 1 and g(x) = sin x. Show that fog ≠ gof.

If f(x) = |x|, prove that fof = f.

If f(x) = 2x + 5 and g(x) = x² + 1 be two real functions, then describe each of the following functions:
(1) fog
(2) gof
(3) fof
(4) f²
Also, show that fof ≠ f²

If f(x) = sin x and g(x) = 2x be two real functions, then describe gof and fog. Are these equal functions?

Let f, g, h be real functions given by f(x) = sin x, g (x) = 2x and h (x) = cos x. Prove that fog = go (fh).

Let  f  be any real function and let g be a function given by g(x) = 2x. Prove that gof = f + f.

   if `f (x) = sqrt(1-x)` and g(x) = `log_e` x are two real functions, then describe functions fog and gof.

  ` if  f : (-π/2 , π/2)` → R and g : [−1, 1]→ R be defined as f(x) = tan x and g(x) = `sqrt(1 - x^2)` respectively, describe fog and gof.

if f (x) = `sqrt (x +3) and  g (x) = x ^2 + 1` be two real functions, then find fog and gof.

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) f²

Also, show that fof ≠ `f^2` .

Let

f (x) =`{ (1 + x, 0≤ x ≤ 2) , (3 -x , 2 < x ≤ 3):}`

Find fof.

 If f, g : R → R be two functions defined as f(x) = |x| + x and g(x) = |x|- x, ∀x∈R" .Then find fog and gof. Hence find fog(–3), fog(5) and gof (–2).

State with reason whether the following functions have inverse :
f : {1, 2, 3, 4} → {10} with f = {(1, 10), (2, 10), (3, 10), (4, 10)}

State with reason whether the following functions have inverse :

g : {5, 6, 7, 8} → {1, 2, 3, 4} with g = {(5, 4), (6, 3), (7, 4), (8, 2)}

State with reason whether the following functions have inverse:

h : {2, 3, 4, 5} → {7, 9, 11, 13} with h = {(2, 7), (3, 9), (4, 11), (5, 13)}

Find f ⁻¹ if it exists : f : A → B, where A = {0, −1, −3, 2}; B = {−9, −3, 0, 6} and f(x) = 3 x.

Find f ⁻¹ if it exists : f : A → B, where A = {1, 3, 5, 7, 9}; B = {0, 1, 9, 25, 49, 81} and f(x) = x²