If f(x)=x-7 and g(x)=sqrt(4-x), what is the domain of the function f/g?
a. (-infinity, 4)
b. (-infinity, 4]
c. (4, infinity)
d. [4, infinity)
e. (4, 7) U (7, infinity)
To find the domain of the function f/g, we need to consider the restrictions on the division.
First, we note that the denominator cannot be equal to zero. In this case, the denominator is g(x) = sqrt(4-x).
To find the values of x for which g(x) = 0, we set the denominator equal to zero and solve for x:
sqrt(4-x) = 0
Squaring both sides, we get:
4-x = 0
Solving for x, we find x = 4.
Therefore, the denominator g(x) is equal to zero when x = 4.
Since the denominator cannot be zero, the function f/g is undefined at x = 4. Hence, the domain of f/g is all real numbers except x = 4.
Therefore, the correct answer is (a) (-infinity, 4).
To determine the domain of the function f/g, we need to find the values of x for which g(x) is defined (not equal to zero) since division by zero is undefined.
In this case, g(x) = √(4-x), so we need to find the values of x for which 4-x is greater than zero (to avoid taking the square root of a negative number).
4 - x > 0
To solve for x, we can subtract 4 from both sides of the inequality:
-x > -4
Multiplying both sides of the inequality by -1, we need to flip the inequality sign:
x < 4
Therefore, the domain of the function f/g is all values of x that are less than 4.
The correct answer is:
a. (-infinity, 4)
(x-7)/sqrt(4-x)
If x >4 , the result is imaginary because the denominator is the square root of a negative number so we know x<4 but we also know that the result is undefined for x = 4
so
x < 4 or from -00 to 4 not including 4