Question

Let f(x)=e^x+3 show that f^-1(x)=ln x-3 can someone explain this to me

Answer 1

Explanation:

For a function ...

  y = f(x)

the inverse function is ...

  x = f(y)

To write that in the form y=f^-1(x), you need to solve for y.

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For your function f(x) = e^x +3 this looks like ...

  x = e^y +3

  x -3 = e^y . . . . . subtract 3

  ln(x -3) = y . . . . . take the natural log

So, we can write ...

  f^-1(x) = ln(x -3)

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Attached is a graph of these functions. As you might guess from the interchange of x and y, a function and its inverse are mirror images of each other across the line y=x.