If $$f\left( x \right)$$ is a periodic function of the period $$k$$ then $$f\left( {kx + a} \right),$$ where $$a$$ is a constant, is a periodic function of the period :
A.
$$k$$
B.
1
C.
$$\frac{k}{a}$$
D.
none of these
Answer :
1
Solution :
$$\eqalign{
& f\left( x \right) = f\left( {x + k} \right) \cr
& \Rightarrow f\left( {kx + a} \right) = f\left( {kx + a + k} \right) = f\left\{ {k\left( {x + 1} \right) + a} \right\} \cr} $$
So, the period is 1.
Releted MCQ Question on Calculus >> Function
Releted Question 1
Let $$R$$ be the set of real numbers. If $$f:R \to R$$ is a function defined by $$f\left( x \right) = {x^2},$$ then $$f$$ is: