Question

How do I find the value of x so f(x)=7

Answer 1

We have a function for which we only have the chart.

We need to find the value of x so that f(x)=7.

NOTE: As we are lookin for the value of x that makes the value of f(x) = 7, we are able to see it in the graph directly:

If we start at y=7, we can draw a line until we intersect the line for f(x). When this happens we draw a vertical line towards the x-axis until we intersect it.

The value of x at that point is the one that makes f(x)=7.

If we can not find the solution by graph, we have to find the equation of the line and clear x for f(x)=7.

SOLUTION WITH EQUATION:

With the information from the chart we have to find the equation.

We can identify two points in the function: (2,0) and (5,7).

Using the 2 known points, we calculate the slope of the line as:

`m=(y_2-y_1)/(x_2-x_1)=(7-0)/(5-2)=(7)/(3)`

Then, we can write the slope-point equation as:

`\begin{gathered} y-y_0=m(x-x_0) \\ y-0=(7)/(3)(x-2) \\ y=(7)/(3)x-(14)/(3) \end{gathered}`

Then, if we know that y=7, we can replace y with this value and calculate x as:

`\begin{gathered} y=7=(7)/(3)x-(14)/(3) \\ 7\cdot3=7x-14 \\ 21=7x-14 \\ 7x=21+14 \\ 7x=35 \\ x=(35)/(7) \\ x=5 \end{gathered}`

Answer: the value of x so that f(x)=7 is x=5.