quotient of function,  formula (f/g)(x) = f(x)/g(x), f(x) = x+3 and g(x) = 2x-5

To find the quotient of the functions \( f(x) \) and \( g(x) \) using the formula:

\[
\left(\frac{f}{g}\right)(x) = \frac{f(x)}{g(x)}
\]

Given:
- \( f(x) = x + 3 \)
- \( g(x) = 2x - 5 \)

Substitute these into the formula:

\[
\left(\frac{f}{g}\right)(x) = \frac{x + 3}{2x - 5}
\]

So, the quotient of the functions is:

\[
\frac{f(x)}{g(x)} = \frac{x + 3}{2x - 5}
\]

### Would you like further details or have any questions?

### Here are 5 related questions for further practice:
1. What is the domain of the function \(\frac{f(x)}{g(x)} = \frac{x + 3}{2x - 5}\)?
2. How does the quotient of functions change if \( g(x) = x^2 - 4x + 4 \)?
3. Calculate \(\left(\frac{f}{g}\right)(2)\) for the given functions \(f(x)\) and \(g(x)\).
4. What is the vertical asymptote of the function \(\frac{f(x)}{g(x)}\)?
5. Simplify the expression \(\frac{f(x)}{g(x)}\) if \( f(x) = x^2 + 4x + 3 \) and \( g(x) = x + 1 \).

### Tip:
Always check the domain of the resulting function when dividing two functions, as the denominator must not be zero.

quotient of function, formula (f/g)(x) = f(x)/g(x), f(x) = x+3 and g(x) = 2x-5

Explore how to find the quotient of two functions, f(x) = x + 3 and g(x) = 2x - 5, using the formula (f/g)(x) = f(x)/g(x). Learn the steps and key algebraic concepts involved, including function division and domain restrictions. Suitable for students in Grades 9-11.

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