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.
answered earlier
solve the problem:
f(x) = -5x+2 and g(x) = 8x^2+9x+7
To determine the domain of a function, we need to consider any restrictions or limitations on the values that the variable can take. Let's go through each case:
(a) Domain of f(x) = 1/x
The function f(x) = 1/x has a restriction on the denominator. Since division by zero is undefined, the denominator cannot be zero. Therefore, the domain of f(x) is all real numbers except for x = 0. So, we can write the domain as:
Domain of f(x) = (-∞, 0) ∪ (0, +∞)
In interval notation, this means that x can be any real number except for 0.
(b) Domain of f(x) X g(x)
When we consider the combination of two functions, we need to consider the domains of both functions. The resulting function will only have values where both original functions are defined.
For f(x) = 1/x and g(x) = x + 3, there are no restrictions on their domains individually. Both functions are defined for all real numbers.
To find the domain of f(x) X g(x), we need to find the overlapping interval where both functions are defined. In this case, since both functions are defined for all real numbers, the overlapping interval is also the domain of the combined function.
Domain of f(x) X g(x) = (-∞, +∞)
So, the domain of the combined function f(x) X g(x) is all real numbers.
Keep in mind that while the domain of f x g is the full set of real numbers, it may be subject to additional restrictions or conditions depending on the specific context or problem being solved.