pre calculus question functions

Question

The function h(x)=1x−3h(x)=1x-3 can be expressed in the form f(g(x))f(g(x)), where g(x)=(x−3)g(x)=(x-3), and f(x)f(x) is defined as: 

f(x)f(x) = 

Answer 1

Given:

h(x) = 1 / (x - 3)

g(x) = x - 3

h(x) = f( g(x) )

Find:

f(x) = ?

Solution:

h(x) = 1 / ( x - 3 ) = f( (x - 3 ) )

Let X = x - 3

f(X) = 1 / X

And just going back to x

∴ f(x) = 1 / x

I hope this helps! Message me in the comments with any questions, comments, or concerns on what I did above!