Is a square root function even or odd?

[DoNotDisturb]

if f(x) = (4x+5)^(1/2) is this an even or odd function

 

[slikmunks]

even, i believe... if it were the 3rd root or 5th root, it'd be odd...

 

[DoNotDisturb]

thx, i'm doing some definite integral problems and got stumped.. thx guys.

 

[slikmunks]

but i don't know, cuz when is a square root function decreasing...? to be even it has to increase and decrease, right?

ignore my other answer, i'm not sure

 

[slikmunks]

why do you need to know that for definite integrals...? what's the problem?

 

[triska]

im not too sure...learned this a long time agoo....
ima dombarse...
evn fxn is when f(-x)=f(x)
odd is when f(-x)=-f(x)

and when u put a neg number in there as x...if x is less than -1.25 then u cnt determine it...cuz u cnt take square root of a neg number...it does not exist...
but id put my chances on odd...imho...
gl

 

[DoNotDisturb]

using the fundamental theorem of calculus: evaluate the integral exactly.

integral from -1 to 1 f(x) = (4x+5)^(1/2)

 

[duke]

hmmm....interesting question....I'm not sure because you get into imaginary numbers....

 

[triska]

integral from -1 to 1 f(x) = (4x+5)^(1/2)

ans:
(8/3)(4x+5)^3/2

now insert 1+-1
and subtract...

[(8/3)10^3/2] - [(8/3)1^3/2] = ? (no calc)

 

[DoNotDisturb]

wouldn't the antiderivative be (1/6)(4x+5)^(3/2) ?

if you differentiate that you get the same function (4x+5)^1/2

 

[schizoid]

I don't know.