How do you find the inverse of f(x)=log(-2x)?

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Answer 1 · 2018-04-06T13:53:23

#f^-1(x)=-1/2 *10^x#

To find the inverse we need to express #x# as a function of #y#:

I am assuming these are common logs, .i.e base 10.

If:

#y=log(x)#

Then:

#10^y=x#

#:.#

#10^y=-2x#

#x=-10^y/2#

Substituting #y=x#

#y=-1/2 *10^x#

#f^-1(x)=-1/2 *10^x#