Question

If f(x) = x + 7 and g(x) = 1/x -13, what is the domain of (f O g)(x)

Answer 1

For this case we have the following functions:

`f (x) = x + 7\\g (x) = \frac {1} {x} -13`

We must find
`(f_ {0} g) (x).` By definition we have to:

`(f_ {0} g) (x) = f (g (x))`

So:

`(f_ {0} g) (x) = \frac {1} {x} -13 + 7 = \frac {1} {x} -6`

By definition, the domain of a function is given by all the values for which the function is defined.

The function
`(f_ {0} g) (x) = \frac {1} {x} -6` is no longer defined when x = 0.

Thus, the domain is given by all real numbers except zero.

Answer:

x nonzero

Answer 2

domain of (f O g)(x) is x≠0

Explanation:

Given:

f(x) = x + 7

g(x) = 1/x -13

Putting g(x) in f(x) i.e f(g(x))

(fog)(x)= 1/x -13 +7

= 1/x-6

Domain of 1/x-6 is x≠0 !