Question

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

Answer 1

The answer is 13. Good Luck

Answer 2

The value of n is:

13

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:

`y-b=(d-b)/(c-a)* (x-a)`

So, let:

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

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

`y-7=\frac{16-7}[9-3}* *(x-3)\\\\y-7=(3)/(2)* (x-3)\\\\y-7=(3)/(2)x-(9)/(2)\\\\y=(3)/(2)x-(9)/(2)+7\\\\y=(3)/(2)x+(5)/(2)`

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

`y=(3)/(2)* 7+(5)/(2)\\\\y=(21)/(2)+(5)/(2)\\\\y=(21+5)/(2)\\\\y=(26)/(2)\\\\y=13`

Hence, the value of n is:

n=13