Let g(x)=2x-7 and h(x)=x+4/3. Perform the indicated operation and state the domain.
To perform the indicated operation, we need to apply the operation stated in the question to the given functions g(x) and h(x). The indicated operation is not specified in the question, so I will assume that we need to find the sum or the sum of functions g(x) and h(x).
The sum of two functions is obtained by adding their respective outputs or values for each x. Therefore, to find the sum of g(x) and h(x), we need to add g(x) and h(x) together.
g(x) = 2x - 7
h(x) = x + 4/3
Sum of g(x) and h(x): g(x) + h(x) = (2x - 7) + (x + 4/3)
To simplify the sum, we combine like terms:
g(x) + h(x) = 2x - 7 + x + 4/3
Combining the x terms:
g(x) + h(x) = 3x - 7 + 4/3
To combine the constants, we need to have common denominators:
g(x) + h(x) = 3x - 21/3 + 4/3
Combining the constants:
g(x) + h(x) = 3x - 17/3
Therefore, the sum of g(x) and h(x) is 3x - 17/3.
Now, let's determine the domain of the sum. The domain of a sum of functions is the intersection of the individual domains of the functions being summed.
The domain of g(x) is all real numbers since it is a linear function.
The domain of h(x) is also all real numbers since it is a linear function.
Therefore, the domain of the sum, g(x) + h(x), is also all real numbers.
In conclusion, the sum of g(x) and h(x) is 3x - 17/3, and the domain of the sum is all real numbers.