Let f: R → R; f(x) = x/c,where c is a constant. Find ​

Question

Let f: R → R; f(x) = \(\frac{x}c\),where c is a constant. Find 

(i) (cf) (x) 

(ii) (c² f) (x)

(iii) \((\frac{1}{c}f)\)(x)

Answer 1

Given:

f(x) = \(\frac{x}c\)

(i) To find: (cf) (x) 

(cf)(x) = c.f(x)

= c. \((\frac{x}c)\)

= x

Therefore, 

(cf)(x) = x 

(ii) To find: (c² f) (x) 

(c² f) (x) = c² . f(x)

= c.\((\frac{x}c)\)

= cx

Therefore, 

(c² f) (x) = cx

(iii) To find: \((\frac{1}{c}f)\)(x)

\((\frac{1}{c}f)\) = \(\frac{1}c\). f(x)

= \(\frac{x}c\)\((\frac{x}c)\)

Therefore,

\((\frac{1}{c}f)\)(x) = \(\frac{x}{c^2}\)