Mathematics

Problem

Let

k: \mathbb R \to \mathbb R

be given by

k(x)=\dfrac{x^{2}+4x+3}{x^{2}-4x+3}

, where the denominator is non-zero. a. (i) State the domain of

k

. b. (ii) Set

y=k(x)

and transform the relation into a quadratic equation in

x

whose coefficients involve

y

. c. (iii) For real solutions in

x

, the discriminant of the quadratic obtained in part (ii) must be non-negative. Use this condition to find all permissible values of

y

. d. (iv) Write the range of the function

k