Question

The table shows values for functions f(x) and g(x) .

x f(x)=2−x g(x)=−2x
−3 8 6
−2 4 4
−1 2 2
0 1 0
1 12 −2
2 14 −4
3 18 −6
What is the solution to f(x)=g(x) ?

Select each correct answer.




x=−3

x=−2

x=−1

x = 0

x = 1

x = 2

x = 3

Answer 1

2-x= -2x

2x-x=-2

x= -2

Answer 2

x= -2 and x= -1

Explanation:

We are given two functions
`f(x)=2^(-x)` and
`g(x)=-2x`.

The table for the values of the functions is given as,

x
`f(x)=2^(-x)`
`g(x)=-2x`

−3 8 6

−2 4 4

−1 2 2

0 1 0

1 12 −2

2 14 −4

3 18 −6

From the table, we see that,

x= -2 and x= -1, the values of the functions are same.

i.e. f(-2) = g(-2) and f(-1) = g(-1).

So, the correct answer for which f(x) = g(x) are x= -2 and x= -1.