finding the inverse graph (2 Viewers)

[Masaken]

how would go about figuring this out (especially if they don't give you the given graphs and in a hypothetical situation ask you to sketch it)? thanks in advance

 

[cossine]

View attachment 36193
how would go about figuring this out (especially if they don't give you the given graphs and in a hypothetical situation ask you to sketch it)? thanks in advance

Unfortunately I don't think there is an easy way to answer the question.

If you calculate the deriative you will find it is cos(x)/|cos(x)|, as an exercise try doing this yourself, it is bit challenging. As a result the answer is d).

As a side note you could eliminate some options by substituting some values e.g. 0, -pi/2, pi/2

 

[Lith_30]

First substitute a point in, it would be good to choose a point that is different for all of the graphs but subbing in is alright

so
hence

thus we can take out options A and B as they do not have the point.

now option C is just so by deduction option D is the correct answer

the proper way to differentiate the two graphs are is to differentiate which reveals that the gradient is a constant. Since there is a constant gradient, the graph must be straight, so the answer is D.

 

[chilli 412]

First substitute a point in, it would be good to choose a point that is different for all of the graphs but subbing in is alright

so
hence

thus we can take out options A and B as they do not have the point.

now option C is just so by deduction option D is the correct answer

the proper way to differentiate the two graphs are is to differentiate which reveals that the gradient is a constant. Since there is a constant gradient, the graph must be straight, so the answer is D.

i got an answer of C by differentiating and getting -1 as the gradient, did you mean to say C or did i mess up?
edit: nvm i accidentally plugged in pi/2 instead -pi/2