Math Problem Statement

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

Solution

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

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

Given:

  • f(x)=x+3f(x) = x + 3
  • g(x)=2x5g(x) = 2x - 5

Substitute these into the formula:

(fg)(x)=x+32x5\left(\frac{f}{g}\right)(x) = \frac{x + 3}{2x - 5}

So, the quotient of the functions is:

f(x)g(x)=x+32x5\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 f(x)g(x)=x+32x5\frac{f(x)}{g(x)} = \frac{x + 3}{2x - 5}?
  2. How does the quotient of functions change if g(x)=x24x+4g(x) = x^2 - 4x + 4?
  3. Calculate (fg)(2)\left(\frac{f}{g}\right)(2) for the given functions f(x)f(x) and g(x)g(x).
  4. What is the vertical asymptote of the function f(x)g(x)\frac{f(x)}{g(x)}?
  5. Simplify the expression f(x)g(x)\frac{f(x)}{g(x)} if f(x)=x2+4x+3f(x) = x^2 + 4x + 3 and g(x)=x+1g(x) = x + 1.

Tip:

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

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Math Problem Analysis

Mathematical Concepts

Algebra
Functions
Rational Expressions

Formulas

Quotient of functions formula (f/g)(x) = f(x) / g(x)

Theorems

Division of functions
Domain restrictions of rational functions

Suitable Grade Level

Grades 9-11