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Question

# Select the correct graph of f(x)=∣∣∣cos∣∣∣x−π4∣∣∣∣∣∣.

A
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B
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C
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Solution

## The correct option is B Given the function f(x)=∣∣∣cos∣∣∣x−π4∣∣∣∣∣∣ Now, the graph of cosx is given as: Now, for this function we have three types of transformations. 1. Shifting the graph by π/4 units to the right will give us the graph of cos(x−π/4) as: Now, we know cos−θ=cosθ, this means the graph of the function will remain same when used with this transformation. Now, if we use the third transformation i.e. |g(x)|, then whatever part of g(x) lying below f(x) will get inverted w.r.t x− axis. Hence, flipping the portion of cos∣∣∣x−π4∣∣∣ lying below the x− axis, we get the graph of f(x)=∣∣∣cos∣∣∣x−π4∣∣∣∣∣∣ as: Thus Option a. is the correct graph of f(x).

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