If f(x) is a linear function, what is the value of n? x f(x) 3 7 7 n 9 16 16 26.5 9 11 13

The value of n is:

13

Step-by-step explanation:

We are given a linear function f(x).

Also we are given a set of values for the function f(x) at different values of x.

The table of values are as follows:

                x                    f(x)

                 3                     7

                 7                      n

                 9                     16

                16                    26.5  

Now, firstly we will find the equation of a line and then put the value of x=7 to find the value of n.

As we know that the equation of a line passing through two point (a,b) and (c,d) is given by:

So, let:

(a,b)=(3,7) and (b,d)=9,16)

Hence, then equation of line i.e. y=f(x) is:

Now, the value of y=f(x) when x=7 is:

Hence, the value of n is:

n=13

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