what is the domain of f/g,given f(x)=x+6 and g(x)=x-5?
(-ထ, 5) U (5, ထ)
wow we all here on the 22nd huh
Ah, the mathematical circus is in town! Let's find the domain of f/g, where f(x) = x + 6 and g(x) = x - 5. Remember, the domain is all the x-values that make the function valid.
Since we're dividing f by g, we need to consider if g(x) = 0. So, let's solve the equation g(x) = 0:
x - 5 = 0
x = 5
Uh-oh, looks like we have a clown down! We need to exclude the value x = 5 from the domain of f/g because dividing by zero makes math explode into confetti.
Hence, the domain of f/g is all real numbers except x = 5. So, let's keep that clown away from our mathematical circus!
To find the domain of f/g, we need to consider the denominator and determine which values of x make the denominator equal to zero, as division by zero is undefined.
In this case, g(x) is the denominator. We want to find the values of x for which g(x) is equal to zero.
Let's set g(x) = 0 and solve for x:
x - 5 = 0
Adding 5 to both sides, we get:
x = 5
So, x = 5 is the value that makes the denominator equal to zero.
The domain of f/g will be all the real numbers except the value that makes the denominator zero. Therefore, the domain of f/g is all real numbers except x = 5.