Question
A function f is defined by f(x)=x^2+4
Evaluate f(3),f(-2),f(x+h) and find the domain and range of f
Evaluate f(3),f(-2),f(x+h) and find the domain and range of f
Answers
Answered by
GPT 3.5
To evaluate f(3), we substitute x = 3 into the function f(x)=x^2+4:
f(3) = 3^2 + 4 = 9 + 4 = 13.
To evaluate f(-2), we substitute x = -2 into the function f(x)=x^2+4:
f(-2) = (-2)^2 + 4 = 4 + 4 = 8.
To evaluate f(x+h), we substitute x + h into the function f(x)=x^2+4:
f(x+h) = (x + h)^2 + 4.
The domain of a function is the set of all possible values of x in the function. Since the function f(x)=x^2+4 is a quadratic function, it is defined for all real values of x. Therefore, the domain of f is all real numbers.
The range of a function is the set of all possible values of f(x) for the given domain. For the function f(x)=x^2+4, the minimum value of x^2 is 0 (for x = 0), so the minimum value of f(x) is 4. Therefore, the range of f is all real numbers greater than or equal to 4.
f(3) = 3^2 + 4 = 9 + 4 = 13.
To evaluate f(-2), we substitute x = -2 into the function f(x)=x^2+4:
f(-2) = (-2)^2 + 4 = 4 + 4 = 8.
To evaluate f(x+h), we substitute x + h into the function f(x)=x^2+4:
f(x+h) = (x + h)^2 + 4.
The domain of a function is the set of all possible values of x in the function. Since the function f(x)=x^2+4 is a quadratic function, it is defined for all real values of x. Therefore, the domain of f is all real numbers.
The range of a function is the set of all possible values of f(x) for the given domain. For the function f(x)=x^2+4, the minimum value of x^2 is 0 (for x = 0), so the minimum value of f(x) is 4. Therefore, the range of f is all real numbers greater than or equal to 4.
There are no human answers yet. A form for humans to post answers is coming very soon!