Statement first, statement forth, and statement seventh are correct because at x = 2.5, f(x) = 0, and it has only one real solution.
What is a function?
It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have a function shown in the picture:
[tex]\rm f(x)=\dfrac{2x-5}{ 2(x^2-1)}[/tex]
By using the identity: a² - b² = (a - b)(a + b)
[tex]\rm f(x)=\dfrac{2x-5}{ 2(x+1)(x-1)}[/tex]
Denominator cannot be zero:
x + 1 ≠ 0 ⇒ x ≠ -1
x - 1 ≠ 0 ⇒ x ≠ 1
x- intercept from the graph: (2.5, 0)
Real zero for the function:
2x - 5 = 0
x = 5/2 = 2.5
The correct statements are:
- f(x) has one real zero because it crosses the x-axis once.
- f(x) has a real zero at 2.5.
- f(x) has an x-intercept at (2.5, 0).
Thus, statement first, statement forth, and statement seventh are correct because at x = 2.5, f(x) = 0, and it has only one real solution.
Learn more about the function here:
brainly.com/question/5245372
#SPJ2
