Question

Determine whether each function is even, odd, or neither.

f(x) = x²_9

g(x) = |x-3

f(x) = 22-1

g(x) = x + x2

Answer 1

Rule for even

`\\ \sf\longmapsto \boxed{\sf f(-x)=f(x),x\in D_f}`

Rule for odd

`\\ \sf\longmapsto \boxed{\sf f(-x)=-f(x),D_f}`

• Here D_f means domain of function.

#1

`\\ \sf\longmapsto f(x)=√(x^2)-9`

• Take x=4

`\\ \sf\longmapsto f(4)=√(4^2)-9=4-9=-5`

`\\ \sf\longmapsto f(-4)=√((-4)^2)=4-9=-5`

Even function✓

#2

`\\ \sf\longmapsto g(x)=|x-3|`

• Take x=2

`\\ \sf\longmapsto g(2)=|2-3|=|-1|=1`

`\\ \sf\longmapsto g(-2)=|-2-3|=|-5|=5`

`\\ \sf\longmapsto -g(2)=-1`

Odd function✓

#3

`\\ \sf\longmapsto f(x)=(x)/(x^2-1)`

• Take x=3

`\\ \sf\longmapsto f(3)=(3)/(3^2-1)=(3)/(9-1)=(3)/(8)`

`\\ \sf\longmapsto f(-3)=(-3)/((-3)^2-1)=(-3)/(8)`

`\\ \sf\longmapsto -f(3)=(-3)/(8)`

Odd function ✓

#4

`\\ \sf\longmapsto g(x)=x+x^2`

• Take x=1

`\\ \sf\longmapsto g(1)=1+(1)^2=2`

`\\ \sf\longmapsto g(-1)=-1+(-1)^2=0`

`\\ \sf\longmapsto -g(1)=-2`

Neither✓