I have to find the domains of these functions and don't know how:
f(x)=SQRT 2x-1
and
f(x)=3/x+4
Help Please!
Hi Bee!
No more worries :)
Domain is simply the possible values of x. Remember you cannot divide by zero, and you cannot get the square root of a negative number.
For f(x)=SQRT 2x-1
Domain=
x>0
For f(x)=3/x+4
Domain=
x cannot equal 4
All you have to do is right an equal-sign with a slash through it.
thanks!!
You're welcome!
Keep those math questions coming, oddly enough, I enjoy answering them. =)
To find the domain of a function, you need to determine the set of possible input values, known as the domain. In other words, you need to identify which values of x are valid inputs for the given functions.
Let's start with the first function:
f(x) = √(2x - 1)
In this case, the square root function (√) has a domain constraint—it can only accept non-negative values or zero as its argument. Thus, the expression inside the square root, 2x - 1, must be greater than or equal to zero:
2x - 1 ≥ 0
To find the domain, we need to solve this inequality for x:
2x ≥ 1
x ≥ 1/2
Therefore, the domain of f(x) = √(2x - 1) is all real numbers greater than or equal to 1/2.
Now, let's move on to the second function:
f(x) = 3/(x + 4)
The only restriction we have in this case is that x + 4 cannot equal zero because division by zero is undefined. So, we need to find the value of x that makes x + 4 equal to zero:
x + 4 = 0
x = -4
Thus, the domain of f(x) = 3/(x + 4) is all real numbers except x = -4. In interval notation, the domain can be expressed as (-∞, -4) U (-4, ∞).