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!