Complete the following table with values of the functions f and g where f is an even function and g is odd ?

Question

Complete the following table with values of the functions f and g where f is an even function and g is an odd function.

x f(x) g(x)

-3 -5 14

-2 5 4

-1 8 9

1

2

3

Answer 1

When a function is even, that means that it has the same value for opposite values of the argument, i.e. f(x)=f(-x)

When a function is odd, that means that it has opposite values for opposite values of the argument, i.e. g(x)=-g(-x)

So, for your table we know that f(-3)=-5, f(-2)=5, f(-1)=8 and f is an even function, so f(3)=f(-3)=-5, f(2)=f(-2)=5, f(1)=f(-1)=8

Then, we know that g(-3)=14, g(-2)=4, g(-1)=9 and g is an odd function, so g(3)=-g(-3)=-14, g(2)=-g(-2)=-4, g(1)= -g(-1)=-9

Hope that helps :)