If f: A ⟶ B is a bijective function and if n(B) = 7, then n(A) is equal to

Let f(x) = \(\sqrt { 1+x^{ 2 } } \) then

If g = {(1,1), (2,3), (3,5), (4,7)} is a function given by g(x) = αx + β then the values of α and β are

f(x) = (x + 1)³ - (x - 1)³ represents a function which is

Represent the function f(x) =\(\sqrt { 2x^{ 2 }-5x+3 } \) as a composition of two functions.

If f(x) = 3x - 2, g(x) = 2x + k and if f o g = f o f, then find the value of k..

Find k if f o f(k) = 5 where f(k) = 2k - 1.

Find x if gff(x) = fgg(x), given f(x) = 3x + 1 and g(x) = x + 3.

The distance S (in kms) travelled by a particle in time ‘t’ hours is given by S(t) = \(\frac { { t }^{ 2 }+t }{ 2 } \). Find the distance travelled by the particle after
(i) three and half hours.
(ii) eight hours and fifteen minutes.

If the function f: R⟶ R defined by 
\(f(x)=\left\{\begin{array}{l} 2 x+7, x<-2 \\ x^{2}-2,-2 \leq x<3 \\ 3 x-2, x \geq 3 \end{array}\right.\)
(i) f( 4)
(ii) f( -2)
(iii) f(4) + 2f(1)
(iv) \(\frac { f(1)-3f(4) }{ f(-3) } \)

Let X = {3, 4, 6, 8}. Determine whether the relation R = {(x, f(x)) | x \(\in \) X, f(x) = x² + 1}. is a function from X to N?