Understanding the Equation: x(t)=2t+2 and Its Inverse Function x(-t)=-2t+2

[dervast]

Hi Let's assume that my function is the following
x(t)=2t+2 -1<=t<0

Which of the following is correct?
x(-t)=-2t+2 -1>=t>0 or
x(-t)=-2t+2 -1>=-t>0 ]
and why

 

[VietDao29]

Hi Let's assume that my function is the following
x(t)=2t+2 -1<=t<0

Which of the following is correct?
x(-t)=-2t+2 -1>=t>0 or
x(-t)=-2t+2 -1>=-t>0 ]
and why

A small hint:
If you let $$\alpha = -t$$, then $$x( \alpha ) = 2 \alpha - 1$$, right? Now what value should $$\alpha$$ take? Or in other words, what's the range for $$\alpha$$? How about -t?
Can you go from here? :)
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By the way, this should be posted in Precalculus Mathematics board.

 

[dervast]

No i am not sure if i can make i :(
I don't know when we have for example the -1<t<2 if i mytliply -1 what changes I should apply to the symbols < >

 

[VietDao29]

No i am not sure if i can make i :(
I don't know when we have for example the -1<t<2 if i mytliply -1 what changes I should apply to the symbols < >

Just change < to >, and vice versa, i.e > to <.
For example, if 1 < t < 2, then -1 > t > -2.
If -1 <= t <= 2, then 1 >= t >= -2.
If you multiply both sides of an inequality by a negative number, then the signs will change. For example: t > 5 <=> -2t < -10.
However, if you multiply both sides of an inequality by a positive number, the signs do not change.
For example: x >= 2 <=> 10x >= 20.
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Now, just answer my question, what's the range for $$\alpha$$? And since $$\alpha = -t$$, what's the range for -t?
Is the second statement correct? From there, is the first statement correct?
Can you go from here? :)

 

[AngelShare]

If you multiply both sides of an inequality by a negative number, then the signs will change. For example: t > 5 <=> -2t < -10.

I just figured I'd post this little note from my lesson page since the thread creator seemed to be confused as to when to flip the inequality sign.

[Copied and pasted here word for word ]

If you must multiply or divide both sides of an inequality by a negative value, the inequality must reverse direction.

 

[dervast]

"If -1 <= t <= 2, then 1 >= t >= -2.
If you multiply both sides of an inequality by a negative number, then the signs will change. For example: t > 5 <=> -2t < -10."

Thx a lot but why in first case whenu u multiply by -1 the t stays sanme?
For me the correct is
If -1 <= t <= 2, then 1 >=- t >= -2.

Finally i agree with that
For example: t > 5 <=> -2t < -10."

 

[VietDao29]

Thx a lot but why in first case whenu u multiply by -1 the t stays sanme?
For me the correct is
If -1 <= t <= 2, then 1 >=- t >= -2.

Yeah, sorry, that's a typo.
So, can you solve the problem now? :)

 

[dervast]

Of course thanks a lot