Consider the rational function f_k(x)= x+5 (x-k)(x-2)

MATHEMATICS · Subjective · GCSE · Mathematics · Algebra · Algebra

Problem

Consider the rational function

f_k(x)=\frac{x+5}{(x-k)(x-2)},

where

k

is a real parameter. (i) State, in set-builder form, the domain of

f_k

for an arbitrary real

k

. (ii) Explain why the choice

k=2

alters the domain and list the excluded value(s) when

k=2

. (iii) Justify, with reasons, whether there exists any real value of

k

for which

f_k

is defined for every real

x