How do you find the inverse of #y=log_4( x/2 +3 )#?

2 Answers
Mar 7, 2016

x = 2(#4^y-3)#

Explanation:

Raise both sides to the power of the base of the logarithm, 4
Use #4^log (x/2+3)#= #x/2+3#...
#4^y=x/2+3#.

Mar 12, 2016

The inverse of a function can be found algebraically by switching the x and y values and solving for y.

Explanation:

#y = log_4(x/2 + 3)#

#x = log_4(y/2 + 3)#

#4^x = y/2 + 3#

#4^x - 3 = y/2#

#2(4^x - 6) = y#

#2(4^x) - 12 = y#

So, #f^-1(x) = 2(4^x) - 12#. Note the #f^-1(x)#: this is important because it shows efficiently and clearly that this is an inverse function. I have been docked marks before for not including this element in my answer.

Practice exercises:

  1. Find the equation of the inverse function.

a). #g(x) =3^(x - 2) + 4#

b). #h(x) =2 log_2(3x - 1)#

Good luck!