In the table below, fill in as many y values as you can if you know that f is an even function, and g is an odd function?

Question

Enter the letter "n" if you cannot fill in a cell
How would I start this problem?

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Answer 1 · 2018-07-28T04:36:29

Kindly refer to Explanation.

Since #f# is even, #f(x)=f(-x)#.

#:. f(-2)=f(2)=-10, and, #.

# f(-1)=f(1)=-7#.

Next, #g# is odd, so, #g(-x)=-g(x)#.

#:. g(-2)=-g(2)=-(-7)=7, and, #

#-g(1)=g(-1)=-6 rArr g(1)=6#.

Observe that, for any odd function like #g# in question,

# AA x, g(-x)=-g(x) :. g(-0)=-g(0)#.

# :. g(-0)+g(0)=0, i.e., g(0)+g(0)=0#.

#:. 2g(0)=0#.

#:. g(0)=0#.

The rest are n.