The table below represents the function f. chart: x l 3 l 4 l 5 l 7 l 8 l f(x) l 7 l 15 l 31 l 127 l 255 l the equation that represents this function is a. f(x)=3^x b. f(x)=3x c. f(x)=2^x-1 d. f(x)=2x+1

The equation that represents this function is:

      Option: C   ( C) )

We are given x and corresponding y-values i.e. y=f(x) in a table form as:

x    l 3 l 4 l   5 l   7   l   8   l

f(x) l 7 l 15 l 31 l 127 l 255 l

Hence, we check each of the following options which satisfies these values.

A)

when x=3

we have:

Hence, option: A is incorrect.

B)

when x=3

we have:

Hence, option: B is incorrect.

C)

when x=3

we have:

when x=4, we have:

when x=5, we have:

when x=7, we have:

when x=8, we have:

Hence each of the values are satisfied.

            Hence, option: C is correct.

D)

when x=4 we have:

Hence, option: D is incorrect.