Show a function is strictly increasing

[quartz badger]

I need to use the defintion of a strictly increasing function and show the given function is increasing

[untold hamlet]

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[wide rain]

Well you can differentiate your function and see that the derivative is strictly positive but I’m assuming you have to use the definition

So take two numbers x and y such that x<y<0

And show that theta(x)<theta(y)

[quartz badger]

i know ive got to do get to that point but im not sure how to start off

how would i being?

begin*

[wide rain]

YLetxythusyoucansaythatxxayysoyhereyousethefactthattheinverseinvertstheinequlitinequalityandthtthatmultiplyingbyinversetheinequlityausingthsquareeachagainusingafterdoisideside

Wtf

My interface is bugged

[quartz badger]

do you think you could retype this? im trying to read figure out what it says but its quite hard

sorry to bother you

[wide rain]

My bad I’ll retype lol sorry

The idea is take x<y<0

That means x=-|x| and y=-|y|

Thus -|x|<-|y|<0 => |x|>|y|>0

=> 1/|x|<1/|y|

Squaring each side 1/x^2<1/y^2

[quartz badger]

thank you

+close