How do you find the inverse of # f(x)=log(x+15)#?

2 Answers

Set #y=f(x)# and solve with respect to #x# hence you get

#y=log(x+15)=>x+15=10^y=>x=10^y-15#

Now it is #f^-1(x)=10^x-15#

Assuming that #log10=1#

Feb 7, 2016

Answer:

#f^-1(x) = 10^x -15 #

Explanation:

For any inverse function of #f(x), f^-1(x)#
#f(f^-1(x)) = x #
#f(f^-1(x+15)) = log(f^-1(x+15)) = log(f^-1(x) + 15) #
#10^x = f^-1(x) +15 #
#f^-1(x) = 10^x -15 #

Alternatively:
#u = x + 15; x = u -15 #
#y = log_b u; b^y = u; b = 10; 10^y = u # substitute for u
#10^y = x+15; x = 10^y -15# replace y by x and write
#f^-1(x) = 10^x -15 # which is exactly as above