Determine the domains of (a)f and
(b) f X g
f(x) = 1/x g(x)= x + 3
For the domain of f I had x > 0 and for f X g I had all real numbers but this was wrong.
1/(x+3)
domain everywhere on x axis except x = -3 where the denominator is zero.
To determine the domain of a function, you need to consider any restrictions on the input values that would cause the function to be undefined.
(a) f(x) = 1/x:
To find the domain of this function, you need to consider where the function is defined. The function 1/x will be undefined if the denominator, x, is equal to zero since division by zero is undefined. Therefore, x cannot be zero.
So the domain of f(x) = 1/x is all real numbers except x = 0. In interval notation, the domain can be expressed as (-∞, 0) ∪ (0, ∞).
(b) f(x) * g(x) = (1/x) * (x + 3):
To determine the domain of the product of two functions, you need to consider the domains of both functions.
As we established earlier, the domain of f(x) = 1/x is all real numbers except x = 0.
The domain of g(x) = x + 3 is all real numbers since there are no restrictions on the input values.
To find the domain of f(x) * g(x), you need to exclude any values that would make either function undefined.
In this case, since f(x) = 1/x is undefined at x = 0, the domain of f(x) * g(x) will also exclude x = 0.
So the domain of f(x) * g(x) is all real numbers except x = 0, which can be expressed as (-∞, 0) ∪ (0, ∞).