How do you find the inverse of log _(1/2) (x+4)=ylog12(x+4)=y?

1 Answer
Rohan A.K
Feb 8, 2016

f^-1(x)=2^-x-4f−1(x)=2−x−4

Explanation:

Given f(x)=log_(1/2)(x+4)f(x)=log12(x+4).
By definition, if f(x)=yf(x)=y then, f^{-1}(y)=xf−1(y)=x

Now, I'm sure you're familiar with log identities and functions and also a bit of law of indices, so
y=log_(1/2)(x+4)implies(1/2)^y=x+4\implies2^-y-4=xy=log12(x+4)⇒(12)y=x+4⇒2−y−4=x
We have f^-1(y)=xf−1(y)=x
So that means f^-1(y)=2^-y-4f−1(y)=2−y−4

Replace yy with xx and there you have it.

Related questions
See all questions in Function Composition
Impact of this question
1593 views around the world
You can reuse this answer
Creative Commons License