How do you find the inverse of #f(x)=2x+ln(x)#?

Answer 1

To find the inverse of the function (f(x) = 2x + \ln(x)), follow these steps:

  1. Replace (f(x)) with (y): (y = 2x + \ln(x)).
  2. Swap (x) and (y): (x = 2y + \ln(y)).
  3. Solve this equation for (y). This may require using techniques such as logarithmic properties or algebraic manipulation to isolate (y).
  4. Once you've found (y), replace it with (f^{-1}(x)) to express the inverse function.

After solving for (y), you'll get (f^{-1}(x)), the inverse of the function (f(x)).

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer 2

Hmm... I don't think this inverse can be written using elementary functions (that is, there isn't a way of using stuff we already know like #sin(x)#, #e^x#, and #x^2.3# to write a function for this).

In order to solve this, you would need some previous calculus experience and a good understanding of integrals. Are you sure you haven't mistyped the question?

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

Not the question you need?

Drag image here or click to upload

Or press Ctrl + V to paste
Answer Background
HIX Tutor
Solve ANY homework problem with a smart AI
  • 98% accuracy study help
  • Covers math, physics, chemistry, biology, and more
  • Step-by-step, in-depth guides
  • Readily available 24/7