Commerce (English Medium) इयत्ता १२ - CBSE Question Bank Solutions

Give examples of two functions f : N → Z and g : Z → Z, such that gof is injective but gis not injective.

If f : A → B and g : B → C are one-one functions, show that gof is a one-one function.

If f : A → B and g : B → C are onto functions, show that gof is a onto function.

 Find fog and gof  if  : f (x) = ex g(x) = loge x .

Find fog and gof  if : f (x) = x2 g(x) = cos x .

Find fog and gof  if : f (x) = |x|, g (x) = sin x .

Find fog and gof  if : f (x) = x+1, g(x) = `e^x`

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Find fog and gof  if : f(x) = sin⁻¹ x, g(x) = x²

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

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.