Let f(x)equals6minusx and g(x)equalsStartFraction 5 Over x EndFraction
. Perform the function operation and then find the domain of the result.
(gminusf)(x)
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.