Question

Which input value produces the same output value for the two functions on the graph?

f(x) = -2/3x+1
g(x) =1/3x-2

Answer 1

The two functions have the same output value
`y=-1` when their input value is
`x=3`

Step-by-step explanation:

The two functions are
`f(x)=-(2)/(3) x+1` and
`g(x)=(1)/(3) x-2`

To determine the same output value for the two functions, let us substitute the values for x-coordinate(input value) in both the functions.

First, let us substitute the values in the function
`f(x)=-(2)/(3) x+1`

For
`x=0` ⇒
`f(0)=1`

For
`x=1` ⇒
`f(1)=(1)/(3)`

For
`x=2` ⇒
`f(2)=-(1)/(3)`

For
`x=3` ⇒
`f(3)=-1`

Similarly, let us substitute the values in the function
`g(x)=(1)/(3) x-2`

For
`x=0` ⇒
`g(0)=-2`

For
`x=1` ⇒
`g(1)=-(5)/(3)`

For
`x=2` ⇒
`g(2)=-(4)/(3)`

For
`x=3` ⇒
`g(3)=-1`

Thus, the two functions have the same output value
`y=-1` when their input value is
`x=3`