Question

Given the two functions `f(x)=2x-1` and `g(x)=-4/3x+9` how do you determine the point that lies in the solution set for both f(x) and g(x)?

Answer 1

Two find the point in the solution set for both these functions equation the two functions (`f(x) = g(x)`) and solve for `x`. See full process below.

Explanation:

Two find the point in the solution set for both these functions equation the two functions (`f(x) = g(x)`) and solve for `x`.

Therefore:

`2x - 1 = -4/3x + 9`

We can now solve for `x`:

`2x - 1 + color(red)(4/3x) + color(blue)(1) = -4/3x + 9 + color(red)(4/3x) + color(blue)(1)`

`2x + color(red)(4/3x) - 1 + color(blue)(1) = -4/3x + color(red)(4/3x) + 9 + color(blue)(1)`

`2x + color(red)(4/3x) - 0 = 0 + 9 + color(blue)(1)`

`2x + color(red)(4/3x) = 10`

`(3/3 xx 2)x + color(red)(4/3x) = 10`

`6/3x + color(red)(4/3x) = 10`

`10/3x = 10`

`color(red)(3)/color(blue)(10) xx 10/3x = color(red)(3)/color(blue)(10) xx 10`

`cancel(color(red)(3))/cancel(color(blue)(10)) xx color(blue)(cancel(color(black)(10)))/color(red)cancel(color(black)(3))x = color(red)(3)/cancel(color(blue)(10)) xx color(blue)(cancel(color(black)(10)`

`x = 3` is the point which lies in the solution set for both functions.