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

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Answer 1 · 2016-01-03T16:14:08

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

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