odd or even (1 Viewer)

[repz]

1/ xsquared +4

is this an odd or even function

(one over x squared plus 4)

 

[shafqat]

try f(-x) and see
if its f(x) its even, which it is in this case

 

[repz]

erm i kinda forgot how.. can anybody give me a full solution i tried but it doesnt look rite?

 

[JamiL]

its even cos x^2 = (-x)^2
ie f(x) = f(-x)

 

[KFunk]

If it's an even function then f(x) = f(-x)

f(x) = 1/(x²+4)
f(-x) = 1/((-x)²+4) = 1/( x²+4)
hence f(x) = f(-x)
and f(x) = 1/(x²+4) is an even function

 

[Slidey]

1/(x^2+4) or 1/x^2 + 4? Oh well I'll do both so you have two examples.

f(x)=1/(x^2+4)
f(-x)=1/((-x)^2+4)=f(x) - even

f(x)=1/x^2 + 4
f(-x)=1/(-x)^2 + 4=f(x) - even

Question: Is f(x)=x^3-7x even or odd?
f(-x)=(-x)^3-7(-x)=-(x^3-7x)=-f(x) - odd

 

[JamiL]

x^2 is even, u can add nething 2 it and it wont affect it
mutiply by a constant and/or an even function and it will still be an even function.

 

[Trev]

its even cos x^2 = (-x)^2
ie f(x) = f(-x)

At least use 'coz' as an abbreviation rather than 'cos', otherwise it screws with my brain if your referring to maths!

 

[dawso]

easiest quick way for one this simple, look at the graph, this is a graph of typical hyperbola, but as it is x squared, it is always positive, then push it up 4, therefore it is symmetrical about y axis, therefore has 2 be even (maybe a bit of 4unit ideas in there but its still simple)