Question

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

Answer 1

Answer:

x=5

Step-by-step explanation:

Answer 2

The value of $x$ so $f(x) = 7$ is 5.

According to the figure, we have a linear function and linear functions have the same slope for all value of $x$, we can determine the value of $f(x)$ for $x = 7$ by means of the equation for the secant line:

$\frac{y_{B}-y_{A}}{x_{B}-x_{A}} = \frac{y_{C}-y_{A}}{x_{C}-x_{A}}$ (1)

Where:

$(x_{A}, y_{A})$, $(x_{B}, y_{B})$ - Known points.

$(x_{C}, y_{C})$ - Expected point.

If we know that $(x_{A},y_{A}) = (2, 0)$, $(x_{B}, y_{B}) = (5, 7)$ and $y_{C} = 7$, then the value of $x_{C}$ is:

$x_{C}-x_{A} = \frac{y_{C}-y_{A}}{y_{B}-y_{A}}\cdot (x_{B}-x_{A})$

$x_{C} = x_{A} + \frac{y_{C}-y_{A}}{y_{B}-y_{A}} \cdot (x_{B}-x_{A})$

$x_{C} = 2 + \frac{7-0}{7-0}\cdot (5-2)$

$x_{C} = 2 + (5-2)$

$x_{C} = 2 + 3$

$x_{C} = 5$

The value of $x$ so $f(x) = 7$ is 5.

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