Calculus How To

Quotient Function: Definition, Excel, Domain

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The term “quotient function” can refer to a few different things:

  1. Quotient Functions (a type of function in calculus)
    1. Definition,
    2. Domain,
    3. Quotient of Two Functions Example.
  2. The Quotient Function in Excel

See also:
What is the Difference Quotient?
What is the Quotient Rule?

1. Quotient Function (Type)

A. Definition

A quotient function is a type of function where two functions are separated by a division sign. For example:

  • f(x)/g(x)
  • X2/x
  • quotient function

B. Domain of a Quotient of Two Functions

The quotient of two functions, f(x) and g(x), has a domain A ∩ B (“A intersected with B” means the set of all points that A and B have in common), excluding where g(x) = 0.

The quotient is given by the following formula:
formula for quotient

Example question: If f(x) = √ (x + 1) and g(x) = 2x + 1:

  1. What is the quotient(q) of f and g?
  2. What is the domain of q?

Part 1: Plug the given functions into the formula:
formula 2

Part 2: Find the domains for the two separate functions. As noted above, the denominator (in this case, 2x + 1) can’t equal zero. In other words, x ≠ -½.

The domain is all points that the two functions have in common.

  • The domain of f(x) = √(x + 1) is A = [-1, ∞). Why? Any number above -1 is fine, but -1 itself would give a denominator of 0. Any number lower than that, and you would be finding the square root of a negative number.
  • The domain of g(x) = B = (-∞, ∞).

The domain of the two functions overlap at [-1, ∞], so that’s the domain of this particular quotient function.

2. Quotient Function in Excel

The format for this function is:
QUOTIENT(numerator, denominator)

Note: A “function” in Excel refers to a predefined formula that performs calculations.

The quotient function in Excel is a bit of an oddity, because it only returns integers. For example, =QUOTIENT(7,2) gives a solution of 3 because QUOTIENT doesn’t give remainders. In other words, you should only use it if you want to discard a remainder. If you wanted to do a straightforward division (with remainder), just use the forward slash. For this example, type =7/3 into a cell instead.


Microsoft Office. Quotient Function. Retrieved October 19, 2019 from:
Tan S. (2008). Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach. Cengage Learning.
Wilson, R. (2013). Much Ado About Calculus: A Modern Treatment with Applications Prepared for Use with the Computer. Springer Science and Business Media. Retrieved OCtober 16, 2019 from:

Stephanie Glen. "Quotient Function: Definition, Excel, Domain" From Calculus for the rest of us!

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