Before the area between these two
functions can be found, they must be
made functions of the same variable.
Convert into .

Ask by Ray Schofield. in the United States

Mar 22,2025

Question

Before the area between these two
functions can be found, they must be
made functions of the same variable.
Convert into .

Ask by Ray Schofield. in the United States

Mar 22,2025

UpStudy AI · Accepted Answer

To convert $$ g(x) $$ into $$ g(y) $$, we need to express $$ x $$ in terms of $$ y $$ using the equation $$ g(x) = \frac{x - 5}{2} $$.

1. Start with the equation for $$ g(x) $$:
   $$
   g(x) = \frac{x - 5}{2}
   $$

2. To express $$ x $$ in terms of $$ g(x) $$, we can rearrange the equation:
   $$
   x - 5 = 2g(x)
   $$
   $$
   x = 2g(x) + 5
   $$

3. Now, substitute $$ g(y) $$ for $$ g(x) $$:
   $$
   g(y) = \frac{(2g(y) + 5) - 5}{2}
   $$
   Simplifying this gives:
   $$
   g(y) = \frac{2g(y)}{2} = g(y)
   $$

However, we need to express $$ g(y) $$ in the form $$ g(y) = [\?] y + [\square] $$.

Since $$ g(x) = \frac{x - 5}{2} $$, we can express it in terms of $$ y $$:
$$
g(y) = \frac{y - 5}{2}
$$

Thus, we can rewrite it as:
$$
g(y) = \frac{1}{2}y - \frac{5}{2}
$$

So, the final form is:
$$
g(y) = \frac{1}{2}y - \frac{5}{2}
$$

In this case, the coefficients are:
- The coefficient of $$ y $$ is $$ \frac{1}{2} $$.
- The constant term is $$ -\frac{5}{2} $$.
$$ g(y) = \frac{1}{2}y - \frac{5}{2} $$

Before the area between these two
functions can be found, they must be
made functions of the same variable.
Convert into .

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Before the area between these two functions can be found, they must be made functions of the same variable. Convert into .

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Before the area between these two
functions can be found, they must be
made functions of the same variable.
Convert into .