If a function fx has fundamental period T- then for any number k- 0- 1- the fundamental period of fkx say T1 will be

It is given that function f(x), have fundamental period T. Now, for any number k∈ (0, 1), we need to find fundamental period of f(kx). Now, we know from the hor ...

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Standard XII

Mathematics

Period of Trigonometric Ratios

If a function...

Question

If a function $f (x)$ has fundamental period $T,$ then for any number $k \in (0, 1),$ the fundamental period of $f (k x)$ say $T_{1}$ will be

> T

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< T

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Solution

The correct option is A $> T$
It is given that function $f (x),$ have fundamental period $T .$
Now, for any number $k \in (0, 1),$ we need to find fundamental period of $f (k x) .$
Now, we know from the horizontal Shrink/Stretch of the graph of any function that for any real number $0 < k < 1$ , the graph of $f (k x)$ will stretch horizontally.
It means the period will increase too.
That means $T_{1} > T$

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If a function f(x) has fundamental period T, then for any number k∈(0,1), the fundamental period of f(kx) say T1 will be

If a function $f (x)$ has fundamental period $T,$ then for any number $k \in (0, 1),$ the fundamental period of $f (k x)$ say $T_{1}$ will be