Find the inverse of the function? : h(x) = log((x+9)/(x−6))
2 Answers
h^(-1)(x) = 3 ( (2e^x + 3) / (e^x - 1) )
Explanation:
We have:
h(x) = log((x+9)/(x−6))
To find
Writing as:
h = log((x+9)/(x−6))
:. (x+9)/(x−6) = e^h
:. x+9 = (x−6)e^h
:. x+9 = xe^h−6e^h
:. xe^h - x = 6e^h + 9
:. x(e^h - 1) = 3(2e^h + 3)
:. x = 3 ( (2e^h + 3) / (e^h - 1) )
Hence, the inverse function is:
h^(-1)(x) = 3 ( (2e^x + 3) / (e^x - 1) )
I have assumed natural logarithms (base e). If base
Explanation:
To find the inverse, let us switch the x and y variables, denoting
Assuming
Adding a base 10 to each side of the equation to cancel out the
Multiplying both sides by
Taking all
I am aware of the other variations in which this answer could be rewritten, but you can work off of this answer to your preference.
Hope this helped!