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?

Enter the letter "n" if you cannot fill in a cellenter image source here
How would I start this problem?

1 Answer
Jul 28, 2018

Kindly refer to Explanation.

Explanation:

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