If x < 1/2 , then you are taking then you are taking the square root of a negative number.Wa1337 said:Homework Statement
If F(x)=√(2x-1) and G(x) = x/(x-2), find G(F(x)) and its domain & range.
The Attempt at a Solution
G(F(x)) = ((√2x-1)/(√(2x-1)-2)
x ≠ 3/2, x </= 1/2
Where do I go from here?
SammyS said:If x < 1/2 , then you are taking then you are taking the square root of a negative number.
Perhaps you meant x ≰ 1/2 . If that's the case, it's more straight forward to say, x > 1/2 .
Your answer of x ≠ 3/2 is incorrect.
How about the range ?
√(4) = 2, so 2x - 1 = 4 will give you 2 - 2 which would be division by zero. That solution is not x = 3/2. Check your algebra.Wa1337 said:Well i thought the denominator could not equal 0, so I did √(2x-1) - 2 ≠ 0 and got x ≠ 3/2.
For the numerator I thought that square roots can't be negative, so they should be >/= 0. So i did √(2x-1) there and got x </= 1/2.
I don't know how to get the range from here, little confused
G(F(x)) is a composition of two functions, where the output of F(x) is used as the input of G(x). It is written as G(F(x)) and can also be read as "G of F of x".
The domain of G(F(x)) is the set of all possible input values for F(x) that will result in a valid output for G(x). To find the domain, you need to look at the domain of F(x) and make sure that those input values are also valid for G(x).
The range of G(F(x)) is the set of all possible output values that can be obtained by plugging in the domain values of F(x) into G(x). In other words, it is the set of all possible outputs of G(x) when the input is restricted to the domain of F(x).
Yes, the domain of G(F(x)) can be different from the domain of F(x). This can happen when the output of F(x) is not a valid input for G(x). In this case, the domain of G(F(x)) will be restricted to only include the input values that will result in a valid output for G(x).
To graph G(F(x)), you can first graph F(x) and then use that graph as the input for G(x). The domain and range can be graphed by looking at the x and y values that are included in the domain and range respectively, and plotting those points on the graph.