What is the domain of the function f/x )= √ 4 x 2?

By Tim Barclay, On 7th February 2022, Under Science and Education
Your domain is all the legal (or possible) values of x , while the range is all the legal (or possible) values of y . So your domain is [−2,2] . Both the 2 and −2 are included, because the stuff inside the square root is allowed to be zero.

In this regard, what is the domain of x 9?

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

Also Know, what is the domain of 9 x 2?

Explanation: y=9x2 is an upside down parabola that has been shifted up 9 units. If it helps, you can rewrite the equation to make y=−x2+9 . The domain of any parabola is all real x, or x∈R .

How do you find the domain?

For this type of function, the domain is all real numbers. A function with a fraction with a variable in the denominator. To find the domain of this type of function, set the bottom equal to zero and exclude the x value you find when you solve the equation. A function with a variable inside a radical sign.

What is the range of 4 x 2?

Thus y=√4x2 is the top half of the circle, which starts at (−2,0) , rises to (0,2) , then descends to (2,0) , showing its range of 0≤y≤2 .
Overall, the steps for algebraically finding the range of a function are:
  1. Write down y=f(x) and then solve the equation for x, giving something of the form x=g(y).
  2. Find the domain of g(y), and this will be the range of f(x).
  3. If you can't seem to solve for x, then try graphing the function to find the range.
Domain. The domain of a function is the complete set of possible values of the independent variable. The domain is the set of all possible x-values which will make the function "work", and will output real y-values.
Another way to identify the domain and range of functions is by using graphs. Because the domain refers to the set of possible input values, the domain of a graph consists of all the input values shown on the x-axis. The range is the set of possible output values, which are shown on the y-axis.
The domain of a function is the complete set of possible values of the independent variable. In plain English, this definition means: The domain is the set of all possible x-values which will make the function "work", and will output real y-values.
Since y is a function of x, the range is made up of the y values. The x values are the inputs and together they make up the domain of the function. The correct answer is that 2 is part of the domain.
For every polynomial function (such as quadratic functions for example), the domain is all real numbers. if the parabola is opening upwards, i.e. a > 0 , the range is y ≥ k ; if the parabola is opening downwards, i.e. a < 0 , the range is y ≤ k .
Example 1:
  1. Find the domain and range of the function y=1x+3−5 .
  2. To find the excluded value in the domain of the function, equate the denominator to zero and solve for x .
  3. x+3=0⇒x=−3.
  4. So, the domain of the function is set of real numbers except −3 .
  5. Interchange the x and y .
  6. x=1y+3−5.
  7. Solving for y you get,
Solution: The domain of a polynomial is the entire set of real numbers. The limiting factor on the domain for a rational function is the denominator, which cannot be equal to zero. The values not included in the domain of t(x) are the roots of the polynomial in the denominator.
The domain of a function is the set of all real values of x that will give real values for y. The range of a function is the set of all real values of y that you can get by plugging real numbers into x. The quadratic parent function is y = x2.
To use the vertical line test, take a ruler or other straight edge and draw a line parallel to the y-axis for any chosen value of x. If the vertical line you drew intersects the graph more than once for any value of x then the graph is not the graph of a function.
The domain of a rational function consists of all the real numbers x except those for which the denominator is 0 . To find these x values to be excluded from the domain of a rational function, equate the denominator to zero and solve for x .