Question

values from the function $g(x)=2\sqrt3{x+3}-1$ are shown in the table. use the table to determine the solution to the equation $2\sqrt3{x+3}-1=-1$.

$x$

$2\sqrt3{x+3}-1$

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$-6$

$-3.8844991$

$-5$

$-3.5198421$

$-4$

$-3$

$-3$

$-1$

Explanation:

Step1: Rewrite the target equation

We start with the given equation:
$$2\sqrt[3]{x+3} - 1 = -1$$
Add 1 to both sides:
$$2\sqrt[3]{x+3} = 0$$

Step2: Match to the function table

The function $g(x) = 2\sqrt[3]{x+3} - 1$. We need $g(x) = -1$, which means we look for the $x$-value where $2\sqrt[3]{x+3} - 1 = -1$. From the table, we check which $x$ gives the corresponding function value.
When $x=-3$:
$$2\sqrt[3]{-3+3} - 1 = 2\sqrt[3]{0} - 1 = 0 - 1 = -1$$
This matches the target equation.

Answer:

$x=-3$