Maths exponential function help please!

I can do part a and b, I get the right answer for all parts except for finding the domain of the inverse function.

I know that the range of f(x) is the domain of the inverse function but how should I go about finding the range of this f(x).

Thanks so much =)

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Reply 1

tallulabellm

OP

10

I am actually so confused, I usually get these correct! I am trying to transform ln(x) , but what it is looking like is that there are no asymptotes in the x plane, is this correct anybody? If it surely then the range is just any real number?

Reply 2

111davey1

14

Original post by Assmaster2

I am actually so confused, I usually get these correct! I am trying to transform ln(x) , but what it is looking like is that there are no asymptotes in the x plane, is this correct anybody? If it surely then the range is just any real number?

What you have to do is take
f(x) = ln x
then first you must f(x+4) which represents a translation to the left by 4
Then replace x with -2x to give f(-2x+4) and this transformation is a reflection in the y and stretch in the x in any order.
I think this is how its done

Reply 3

tallulabellm

OP

10

Original post by 111davey1

What you have to do is take
f(x) = ln x
then first you must f(x+4) which represents a translation to the left by 4
Then replace x with -2x to give f(-2x+4) and this transformation is a reflection in the y and stretch in the x in any order.
I think this is how its done

Yes I understand the transformation, but what I am wondering is what the range would be. Would it be any real number, because there are no horizontal asymptotes for ln(x)?

Reply 4

111davey1

14

Original post by Assmaster2

Yes I understand the transformation, but what I am wondering is what the range would be. Would it be any real number, because there are no horizontal asymptotes for ln(x)?