Question

Let `f(x) = -1 /(x - 7)` and `g(x) = 8-x^2`, how do you find each of the compositions and domain and range?

Answer 1

The composition of two functions is really just substituting one function as the x value of the other. See example below for detailed explanation.

Explanation:

Example: Find f(g(x))

This means that we must replace x in f(x) for g(x):

=`-1/(8 - x^2 -7)`

= `-1/(1 - x^2)`

= `1/(x + 1 X x - 1)`

The domain on this function would be x cannot be 1 or -1 and the range would be y cannot be 0.