Hey! I have a domain and range question! I don't remember how to get these, can you help? How do you calculate the domain and range of these?
What's the domain and range of each?
a. f(x)= 1/x=3
b. g(x)= [square root of] (x+6)
c. h(x)= x^3+2x+5
Thanks for help!:)
a) Don't you mean 1/(x-3) ?
b. The domain is all numbers greater than or equal to -6, since you cannot take a suare root of a negative numbers.
The range is 0 and all positive numbers.
c. x and h(x) can be any real number, positive or negative
Thanks!:)
f(x) = x2-4
Of course! I'm here to help. Calculating the domain and range involves understanding the behaviors and limitations of the given functions. Let's go through each function and find their respective domains and ranges:
a. f(x) = 1/(x+3):
To find the domain of this function, we need to identify any restrictions that may exist. Here, the only restriction is that the denominator (x+3) cannot be equal to zero because division by zero is undefined. So, to find the domain, we solve the equation x+3=0 and exclude this value from the domain. In this case, x cannot be -3. Therefore, the domain for f(x) is all real numbers except -3.
Now, to find the range, we need to consider the values that f(x) can take. In this case, f(x) is a rational function, which means its range includes all real numbers except 0. So, the range for f(x) is all real numbers except 0.
b. g(x) = √(x + 6):
To determine the domain of this function, we need to ensure that the expression inside the square root (√) is non-negative because taking the square root of negative numbers is undefined for real numbers. So, we set x + 6 ≥ 0 and solve for x. It gives us x ≥ -6. Therefore, the domain for g(x) is all real numbers greater than or equal to -6.
Next, let's find the range for g(x). Since the square root of any non-negative number is always non-negative, the range of the square root function is also non-negative. Therefore, the range for g(x) is all real numbers greater than or equal to 0.
c. h(x) = x^3 + 2x + 5:
Determining the domain of this function involves considering all possible values that x can take. In this case, x can be any real number. Thus, the domain for h(x) is all real numbers.
To find the range, we need to consider the behavior of the function. The function h(x) is a polynomial function, and polynomials have a range that includes all real numbers. So, the range for h(x) is all real numbers.
I hope this helps! Let me know if you have any further questions or need any additional clarification.