Question #3bf15

1 Answer
Dec 4, 2017

See below.

Explanation:

#f(x)=sqrt(x-4)# and #g(x)=x^2+4#

If these are inverse of each other, then we would expect:

#f(g(x)=x# for all #x# in domain #g#

#g(f(x)=x# for all #x# in domain #f#

This means that every input returns the input.

#f(g(x))=sqrt(x^2+4-4)=x#

#g(f(x))=(sqrt(x-4))^2+4=x#

So they are inverses.

This more formal way might seem a little confusing at first, but if you look at it in the following way, it starts to make sense. Let's use a simple example:

#f(x)=x+1# and #g(x)=x-1#

These are obviously inverses of each other.

If we put into #f(x)# some value of #x#, let's say #x=3#

#f(3)=4#

If we then put this value into #g(x)#:

#g(4)=3# ( This is the original value of #x# put into #f(x)# )

So:

#g(f(x)=x#

If we put into #g(x)# some value of #x#, let's say #x=5#

#g(5)=4#

We then put this into #f(x)#.

#f(4)=5#

So: #f(g(x))=x#

Hope this helps.