Question

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

Answer 1

Answer:

domain of (f O g)(x) is {x|x≠0}

Step-by-step 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|x≠0} !

Answer 2

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