The function which is equivalent to f(x)=16[tex]x^{2}[/tex]-1 is f(x)=(4x+1)(4x-1) and x intercept lies at (1/4,0),(1/4,0).
What is function?
Function is relationship between two or more that are variables expressed in equal to form. In a function each value of x must have a corresponding value of y.
How to solve a function?
The function which is being give to us is f(x)=16[tex]x^{2}[/tex]-1 and we have to find the equivalent function that best shows the x intercepts on the graph.
f(x)=16[tex]x^{2}[/tex]-1
We can find the factors of the expression 16[tex]x^{2}[/tex]-1.
f(x)=[tex](4x)^{2} -(1)^{2}[/tex]
=(4x+1)(4x-1) [We know that [tex]a^{2} -b^{2}[/tex]=(a+b)(a-b)]
Now we have to find the x intercept. We know that x intercept is a point at which the line touches the x axis means y coordinate will be zero at that point. So we have to put the value of f(x)=0
(4x-1)(4x+1)=0
It can be like under:
4x-1=0,4x+1=0
x=1/4,-1/4
Hence the function which is equivalent to f(x)=16[tex]x^{2}[/tex]-1 is f(x)=(4x+1)(4x-1) and x intercept lies at two points (-1/4,0,(1/4,0).
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