BlingBlong Group Title I Have the function (ln(x)-1)^(1/2) determine the range and inverse of the function. I determined the inverse to be: e^(x^(2)-1) How do I find the domain and range of this function can someone explain this to me I'm lost 2 years ago 2 years ago

1. watchmath Group Title

why you deleted your post before. Your domain was correct. But the range is $$[0,\infty)$$. Since $$\ln(x)-1$$ take values from $$-\infinity$$ to $$\infinity$$. So square root of that (the one that make sense) can take value from 0 to infinity.

2. BlingBlong Group Title

You can't input 0 or any negative value into ln(x) it is not possible

3. BlingBlong Group Title

I came up with the domain of [e, +infinity) and a Range of [(2)^(1/2), infinity)

4. JamesJ Group Title

The domain is x such that $\ln x - 1 \geq 0$ i.e., $$x \geq e$$. Hence the range is $$[0, \infty)$$ because the function is everywhere increasing, unbounded and evaluated at $$x = e$$ the function is zero.

5. BlingBlong Group Title

How can an exponential function be zero

6. JamesJ Group Title

Your inverse is wrong. Write the equation x = f(y) and solving for y, we have $x = \sqrt{\ln y - 1}$ $x^2 + 1 = \ln y$ $y = e^{x^2 + 1}$ This is the inverse function

7. BlingBlong Group Title

oh ok I get it now :) that is why i was messed up

8. BlingBlong Group Title

Everyone of my problems there is such a simple answer for :(

9. asnaseer Group Title

Don't worry @BlingBlong - we can only learn through mistakes.

10. JamesJ Group Title

Notice that the domain of the inverse function is the range of the function hence the range is the the subset of the reals, $$[0, \infty)$$ despite the fact that the formula for the inverse makes sense for all real numbers.

11. JamesJ Group Title

I.e., with $$f(x) = \sqrt{ \ln x - 1 }$$, $f : [e,\infty) \rightarrow [0,\infty)$ and $f^{-1} : [0,\infty) \rightarrow [e,\infty)$

12. BlingBlong Group Title

so x in the inverse function is just y in the function

13. BlingBlong Group Title

ok I got it thanks for clarifying that for me james

14. JamesJ Group Title

right ... the way you can find the inverse of a function f is to solve the equation x = f(y) for y.