Let ​f(x)equals6minusx and ​g(x)equalsStartFraction 5 Over x EndFraction

Question

. Perform the function operation and then find the domain of the result.
​(gminus​f)(x)

Answer 1

To perform the operation ​(g-f)(x), we need to subtract ​f(x) from ​g(x):

g(x) = 5/x
f(x) = 6 - x

(g - f)(x) = g(x) - f(x)

Substitute the functions:
(g - f)(x) = 5/x - (6 - x)
(g - f)(x) = 5/x - 6 + x
(g - f)(x) = x + 5/x - 6

To find the domain of this result, we need to consider the limitations on the input values for which the function is defined. Since there is a division by x in the function, x cannot be equal to 0. Therefore, the domain is all real numbers except x = 0. The domain of (g - f)(x) is all real numbers except x = 0.