Science (English Medium) कक्षा १२ - CBSE Question Bank Solutions for Mathematics

If f : R → R, g : R → are given by f(x) = (x + 1)² and g(x) = x² + 1, then write the value of fog (−3).

Let A = {x ∈ R : −4 ≤ x ≤ 4 and x ≠ 0} and f : A → R be defined by \[f\left( x \right) = \frac{\left| x \right|}{x}\]Write the range of f.

Let \[f : \left[ - \frac{\pi}{2}, \frac{\pi}{2} \right] \to\] A be defined by f(x) = sin x. If f is a bijection, write set A.

Let f : R − {−1} → R − {1} be given by\[f\left( x \right) = \frac{x}{x + 1} . \text{Write } f^{- 1} \left( x \right)\]

Let `f : R - {- 3/5}` → R be a function defined as `f  (x) = (2x)/(5x +3).` 

f^-1 : Range of f → `R -{-3/5}`.

Let f : R → R, g : R → R be two functions defined by f(x) = x² + x + 1 and g(x) = 1 − x². Write fog (−2).

Let f : R → R be defined as  `f (x) = (2x - 3)/4.` write fo f^-1 (1) .

Let f be an invertible real function. Write ( f^-1  of ) (1) + ( f^-1  of ) (2) +..... +( f^-1 of ) (100 )

Let A = {1, 2, 3, 4} and B = {a, b} be two sets. Write the total number of onto functions from A to B.

Write the domain of the real function

`f (x) = sqrtx - [x] .`

Write the domain of the real function

`f (x) = sqrt([x] - x) .`

Write the domain of the real function

`f (x) = 1/(sqrt([x] - x)`.

Write whether f : R → R, given by `f(x) = x + sqrtx^2` is one-one, many-one, onto or into.

If f(x) = x + 7 and g(x) = x − 7, x ∈ R, write fog (7).

What is the range of the function

`f (x) = ([x - 1])/(x -1) ?`

If f : R → R be defined by f(x) = (3 − x³)1/3, then find fof (x).

If f : R → R is defined by f(x) = 3x + 2, find f (f (x)).

Let A = {1, 2, 3}, B = {4, 5, 6, 7} and let f = {(1, 4), (2, 5), (3, 6)} be a function from A to B. State whether f is one-one or not.

If f : {5, 6} → {2, 3} and g : {2, 3} → {5, 6} are given by f = {(5, 2), (6, 3)} and g = {(2, 5), (3, 6)}, then find fog.    [NCERT EXEMPLAR]