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Question

# Period of the function f(x)=4sec(3x−π4) is

A
4π3
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B
2π
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C
3π4
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D
2π3
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Solution

## The correct option is D 2π3Let us first draw the graph y=4sec(3x−π4). The fundamental function involved is secx whose period is 2π and graph is given by Apply a stretch by 3 units to the graph of secx to get y=sec3x as shown below We can see that period of y=sec3x is 2π3. or we can also use the technique, if T is period of f(x) then period of f(ax) is T|a|. Now, apply the horizontal shift to above graph, to get y=sec(3x−π4) as shown below Here, we can see horizontal shift doesnot effect the period and period remains same as 2π3. Now stretch the above graph by 4 units to get the graph of y=4sec(3x−π4) as shown below Again we can see that vertical stretch doesnot effect the period and period remains same as 2π3.

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