Find the Domain, Range, Inverse of the function.

Algebra
Tutor: None Selected Time limit: 1 Day

f(x)=3^(x-2)+1

This makes sense to me that the domain is all Real numbers.

When I graph this function the range tells me that it is y 1

To make this easy for me I set:

y=3^(x-2)+1

Subtract 1

y-1=3^(x-2)

This is where I'm stuck..do I divide by the 3? Or do I need to do Logbase ..steps would help me out a lot. Thank you.

Jun 16th, 2015

Hi !

f(x) = 3^(x-2) + 1

We can also write it as

y = 3^(x - 2) + 1

To find inverse, we solve for x

y - 1 = 3^(x - 2)

taking log, we get

ln(y - 1) = ln(3^(x - 2))

ln(y - 1) = (x - 2)ln(3)

ln(y - 1) = - 2ln(3) + xln(3)

Adding 2ln(3) on both sides, we get

ln(y - 1) + 2ln(3) = - 2ln(3) + xln(3) + 2ln(3)

ln(y - 1) + 2ln(3) = xln(3)

Now dividing by ln(3) on both sides, we get

[ ln(y - 1) + 2ln(3) ] / ln(3) = xln(3) / ln(3)

x = [ ln(y - 1) + 2ln(3) ] / ln(3)

now substitute y = x

   = [ ln(x - 1) + 2ln(3) ] / ln(3)

Which is the inverse of the function.

Domain of the function is " All Real Numbers "

Range is " {y ϵ R : y > 1} "

Hope you get it. Thanks :)
Jun 16th, 2015

Did you get it? The inverse of the function, dear?

Jun 16th, 2015

I believe so. You did an amazing job at explaining the steps to get the inverse of the function. Just so I'm clear on everything, what would be the Domain and Range of the inverse?

[ln(y-1)+2ln(3)]/ln3

Jun 16th, 2015

Domain of inverse is " { x ϵ R : x > 1} "

Range of the inverse is " All Real Numbers "

Jun 16th, 2015

Which is just the opposite :D You answered all of my questions and explained it easier than my professor. Great work, thank you so much!

Jun 16th, 2015

Yes! the opposite from real function. Pleasure to help you. Post any other questions If you have. I will do my best to help you. Please Best me,Thanks :)

Jun 16th, 2015

Rated 5 and commented. Thanks again, take care! :)

Jun 16th, 2015

Didn't get the review. 

Jun 16th, 2015

Ok no problem. Thanks :)

Jun 16th, 2015

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