Question

Select the correct graph of $f\left(x\right)=|\cos |x-\frac{\pi }{4}||.$

• A.
• B.
• C.

Answer 1

The correct option is B

Given the function $f\left(x\right)=|\cos |x-\frac{\pi }{4}||$
Now, the graph of $\cos x$ is given as:

Now, for this function we have three types of transformations.
1. Shifting the graph by $\pi /4$ units to the right will give us the graph of $\cos (x-\pi /4)$ as:

Now, we know $\cos -\theta =\cos \theta ,$ this means the graph of the function will remain same when used with this transformation.

Now, if we use the third transformation i.e. $|g\left(x\right)|,$ then whatever part of $g\left(x\right)$ lying below $f\left(x\right)$ will get inverted w.r.t $x-$ axis.
Hence, flipping the portion of $\cos |x-\frac{\pi }{4}|$ lying below the $x-$ axis, we get the graph of $f\left(x\right)=|\cos |x-\frac{\pi }{4}||$ as:


Thus Option a. is the correct graph of $f\left(x\right).$