1.
If:
f(x)= x , for x≤1 & x^2 ,for x>1
Then,
What is the inverse of f(x)?
1- x , for x≤1 & √x ,for x>1
2- -x , for x≤1 & -√x ,for x>1
3- 1/x , for x≤1 & 1/x^2 ,for x>1
4- -1/x , for x≤1 & -1/x^2 ,for x>1
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2.
If:
y= ln {(x+1)/(x-1)}
Then,
What is the inverse of y?
1- (2e^x-1)/(2e^x+1)
2- (e^x+1)/(e^x-1)
3- (e^x-1)/(e^x+1)
4- (e^x-2)/(e^x+2)
Replies
Solution:
1.
F(2) = 4
Then we must have:
{f(4)}^(-1) = 2
So, only option 1 can be its answer.
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2.
y= ln {(x+1)/(x-1)}
e^y = (x+1)/(x-1)
e^y (x-1) = (x+1)
x(e^y) – {(e^y) -1} = x
x- x(e^y) = -(e^y) -1
x(1-e^y) = -(e^y) -1
x = (e^y +1) / (e^y -1)
=>
The answer is:
y = (e^x+1)/(e^x-1)
Geometry!
Very nice field!!
Why not!
Sure.
WOW!!
Sue!
They are right!!
You are very smart that can answer them in this condition too!
Well done dear!