Question

Express the function h(x)= 1/x-6 in the form of f o g. If g(x)=(x-6), find the function f(x).

Answer 1

Answer:

f(x) = 1/x

Step-by-step explanation:

h(x) = f(g(x)) = f(x-6) = 1/x-6

1/x-6 could only be accomplished if f(x) = 1/x

Assuming f(x) = 1/x and g(x) = x-6, f(g(x)) = f(x-6) = 1/x-6

Since f(g(x)) = 1/x-6 = h(x), we've proven that f(x) = 1/x.

Answer 2

The given functions are illustrations of a composite function, where the function f(x) is:

$f(x) = \frac{1}{x}$

Given that:

$h(x) = \frac{1}{x - 6}$

$g(x) = x - 6$

f o g can be written as f(g(x))

So, we have:

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

Rewrite as:

$f(g(x)) = \frac{1 }{x - 6}$

Substitute g(x) for x - 6

$f(g(x)) = \frac{1 }{g(x)}$

Replace g(x) with x

$f(x) = \frac{1}{x}$

Hence, the function f(x) is: $f(x) = \frac{1}{x}$

Read more about composite functions at:

https://brainly.com/question/8776301