Question

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

Answer 1

Your answer would be C, F(x)=2^x-1.

Answer 2

The equation that represents this function is:

Option: C ( C)
`F(x)=2^x-1` )

Explanation:

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)

`F(x)=3^x`

when x=3

we have:

`F(3)=3^3\\\\\\F(3)=27\\eq 7`

Hence, option: A is incorrect.

B)

`F(x)=3x`

when x=3

we have:

`F(3)=3* 3\\\\\\F(3)=9\\eq 7`

Hence, option: B is incorrect.

C)

`F(x)=2^x-1`

when x=3

we have:

`F(3)=2^3-1\\\\\\F(3)=7`

when x=4, we have:

`F(4)=2^4-1\\\\F(4)=15`

when x=5, we have:

`F(5)=2^5-1\\\\F(5)=31`

when x=7, we have:

`F(7)=2^7-1\\\\F(7)=127`

when x=8, we have:

`F(8)=2^8-1\\\\F(8)=255`

Hence each of the values are satisfied.

Hence, option: C is correct.

D)

`F(x)=2x+1`

when x=4 we have:

`F(4)=2* 4+1\\\\F(4)=9\\eq 15`

Hence, option: D is incorrect.