Question

What is the solution to f(x)=g(x) ? Select each correct answer.

x f(x)=0.5x g(x)=−0.5x+1
−2 4 2
−1 2 32
0 1 1
1 12 12
2 14 0

Answer 1

The solution of f(x)=g(x) is x=0

Explanation:

We need to find the solution of f(x)=g(X) using table.

First we draw the table for difference value of x

`x`
`f(x)=0.5^x`
`g(x)=-0.5x+1`

`-2`
`0.5^(-2)=4`
`-0.5(-2)+1=2`

`-1`
`0.5^(-1)=2`
`-0.5(-1)+1=(3)/(2)`

`0`
`0.5^(0)=1`
`-0.5(0)+1=1`

`1`
`0.5^(1)=(1)/(2)`
`-0.5(1)+1=(1)/(2)`

`2`
`0.5^(2)=(1)/(4)`
`-0.5(2)+1=0`

Solution of the equation when both function will get same value for same value of x.

`0.5^x=-0.5x+1`

`0.5^0=-0.5(0)+1`

`1=1`

TRUE

In table we can see at x=0

f(0)=1

g(0)=1

f(0)=g(0)=1

Hence, The solution of f(x)=g(x) is x=0

Answer 2

(0,1)

Explanation:

To find when f(x)=g(x), then look for a value that is the same for both functions in the table. 1 occurs twice for the same x value. This is when they are equal. The solution is (0,1).