Discover Inverse Functions for Equations with Exponents and Logarithms

[IDontKnow430]

Homework Statement

a.)y=sqrt(2^x -1) . I tried:

b.)y=log(sqrt(2^x -2)) and

c.)y=log^3 (2-sqrt(x)).

Homework Equations

The Attempt at a Solution

x=sqrt(2^y -1)

x^2 = 2^y -1

2^y = x^2 +1

y=log2(x^2 +1)

y=2 log2(x+1) is that correct result?

regarding b and c I am just lost :/. Will appreciate any help

 

[member 587159]

Homework Statement

a.)y=sqrt(2x -1) . I tried:

b.)y=log(sqrt(2x -2)) and

c.)y=log3 (2-sqrt(x)).

Homework Equations

The Attempt at a Solution

x=sqrt(2y -1)

x2 = 2y -1

2y = x2 +1

y=log2(x2 +1)

y=2 log2(x+1) is that correct result?

regarding b and c I am just lost :/. Will appreciate any help

What are the domains and codomains of those functions? This is quite important.

 

[IDontKnow430]

x e R a.) x>=0 b.)x>1 c.) 0<=x<4.
I had wrongly formated question before, lost few ^symbols while posting, should be fixed now.

 

[epenguin]

Well maybe you have not sorted the actual writing yet. If a is the question, you seem to have just interchanged x and y for no reason. Then squaring both sides is the right idea, but after that check your reasoning. We'll need to see it written out properly to comment more.

 

[SammyS]

Homework Statement

a.) y=sqrt(2^x -1) . I tried:

b.) y=log(sqrt(2^x -2)) and

c.) y=log^3 (2-sqrt(x)).

Homework Equations

The Attempt at a Solution

x=sqrt(2^y -1)

x^2 = 2^y -1

2^y = x^2 +1

y=log2(x^2 +1)

y=2 log2(x+1) is that correct result?

regarding b and c I am just lost :/. Will appreciate any help

Hello IDontKnow430, Welcome to PF.

In the future: Please include a complete statement of your problem in the body of your Originating Post, no matter what you state in the title.

It the domains you list in post #3 does make these functions one-to-one. That's good and necessary if they are to have an inverse.

You should determine the range for each of the given functions. That will help you to find domains for the inverse functions which make them one-to-one.

The last step in your attempt with part (a) is incorrect.