Question

= f(x) g(x) { x + 5 g x + 7 = 8 6 4 2 -8 -6 -4 -2 1-24 Clear All Draw: For what value of x is f(x) = g(x)?

Answer 1

The quetion provides two functions, that is f(x) and g(x).

For what value of x is f(x) = g(x)

We can solve this by simply equating both functions, as shown below;

`\begin{gathered} f(x)=(2)/(3)x+5 \\ g(x)=(4)/(3)x+7 \\ f(x)=g(x)\text{ now becomes;} \\ (2)/(3)x+5=(4)/(3)x+7 \\ \text{Collect all like terms and we'll have} \\ (2)/(3)x-(4)/(3)x=7-5 \\ (2x-4x)/(3)=2 \\ -(2x)/(3)=2 \\ \text{Cross multiply and we'll have} \\ -x=(2*3)/(2) \\ -x=3 \\ \text{Multiply both sides by -1 and we'll have} \\ -x(-1)=3(-1) \\ x=-3 \end{gathered}`

The answer is, when x = 3

**Note**

Thi can also be solved graphically and at the point where the graph of both function intersect, we'll have our answer. The graphs of f(x) and g(x) is shown below;

Note that the blue line represents

`f(x)=(2)/(3)x+5`

The green line represents

`g(x)=(4)/(3)x+7`

Observe carefully that both graphs intersect at the point -3.

Therefore, the value of x that makes f(x) = g(x) is -3