Question about functions

Question

Hey everybody!
I can't understand the explanation about this task, if anyone can help me with it?
The task is in Uploaded attachment.
Thanks a lot!

BrushMyQuant · Answer

Hi,

Approach for the function questions:
1. You need to plugin values of the functions given in each option in the question given and see if that option satisfies the question expression.
2. If it does then that's your answer else
3. move to next option and follow the same exercise

In the given questions they are asking you if g(a) = g(3-a) and they have given you 5 options. What you need to do is plugin the options in the question and see if it satisfies.
Option 1:
g(a) = 2a
so, g(3-a) =2(3-a)  
= 6-2a
question : Is g(a) = g(3-a)
substitute the values of g(a) and g(3-a) we get
2a = 6-2a ? we dont know if it is equal  
so, A is not the answer.

Moving on to B
g(a) = a^2
g(3-a) = (3-a)^2
here also, g(a) can be or cannot be equal to g(3-a)
so, B is not the answer.

Moving on to C
g(a) = a(3-a)
g(3-a) = (3-a) ( 3-(3-a)) = (3-a) (3-3 + a) = (3-a)a = a(3-a)
g(a)=g(3-a) for all values of a so, C is the answer.

Similarly you can check for D and E and you will get that g(a) can be or cannot be equal to g(3-a)

hence, answer will be C

Also, in these kind of questions what you can do is
Only for those functions g(a) will be equal to g(3-a) which are symmetric in terms of a and (3-a), or functions in which "a" and (3-a) have the same power and stuff
As you see in option C g(a) = a*(3-a) both "a" and (3-a) have same power 1

also, if you had g(a) = a/(a * (3-a)) then also you have same powers of "a" and (3-a) which is -1 so for this also g(a) will be equal to g(3-a)

hope it helps!

Question about functions

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