How do you invert a logarithmic function?

1 Answer
Feb 23, 2016

Answer:

You must switch the x and y coordinates. See example below.

Explanation:

Find the inverse of #ƒ(x) = log_2(x + 4)#

#y = log_2(x + 4)#

#x = log_2(y + 4)#

2 is the base, x is the exponent, and y + 4 is the answer.

#y + 4 = 2^x#

#y = 2^x - 4#

#ƒ^(-1)(x) = 2^x - 4#

Essentially, the inverse of a logarithmic function is an exponential function.

You could also have found the inverse graphically by reflecting the image of the function over the line y = x. For example, if the point (8, 9) is on the graph of #y = ƒ(x)#, then the point (9, 8) is on the graph of #y = ƒ^(-1)(x)#

Practice exercises:

  1. Find the inverses of the following functions.

a) #g(x) = log_4(2x + 5)#

b) #h(x) = 2^(x - 3) - 4#

Good luck!