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Quizzes > Mathematics

Function Notation Quiz: Practice f(x), Domain, and Composites

Quick, free function notation practice. Instant results.

Editorial: Review CompletedCreated By: Murdoch Dubai Student LifeUpdated Aug 26, 2025
Difficulty: Moderate
2-5mins
Learning OutcomesCheat Sheet
Paper art illustration of function notation quiz, with graphs equations domain composite functions on coral background

This function notation quiz builds your skills with f(x), evaluating functions, domain and range, and simple composites. Get instant feedback so you can spot mistakes and improve faster. For more on chaining functions, try the composition of functions quiz, explore graphs with graphing functions practice, or do a quick check-up with the functions unit test.

If f(x) = 2x + 3, what is f(2)?
4
8
7
5
To evaluate f(2), substitute x = 2 into 2x + 3 to get 2(2) + 3 = 7. This is a direct application of function notation. For more on evaluating linear functions, see .
Given f(x) = x^2 - 5, what is f(a + 1)?
a^2 + 2a - 6
a^2 - 5a + 1
(a + 1)^2 - 5
a^2 + 2a - 4
Substitute x = a + 1 into x^2 - 5 to get (a + 1)^2 - 5. You could expand it further if needed. This demonstrates how to apply function notation to expressions. More examples are available at .
What is the domain of f(x) = 1/(x - 4)?
All real numbers
x ? 4
x > 4
x ? 4
The function has a denominator x - 4, which cannot be zero. Therefore, x ? 4. All other real x are allowed. For an explanation of domain restrictions, see .
If f(x) = -3x + 4, what is f(-1)?
-7
1
7
0
Substitute x = -1 into -3x + 4 to get -3(-1) + 4 = 3 + 4 = 7. This uses basic arithmetic in function evaluation. See more examples at .
Given f(x) = x + 2 and g(x) = 3x, what is (f ? g)(2)?
8
7
10
6
Compute g(2) = 3·2 = 6, then f(6) = 6 + 2 = 8. Composition applies the inner function first and then the outer function. For more on compositions, see .
What is the domain of f(x) = ?(3x - 6)?
All real numbers
x ? 2
x > 2
x ? 2
Inside the square root, 3x - 6 must be ? 0, so 3x ? 6, which gives x ? 2. Only those x values produce real outputs. For domain of radical functions, see .
If f(x) = 5x - 5, for what x does f(x) = 10?
x = 3
x = 4
x = 2
x = 5
Set 5x - 5 = 10, so 5x = 15 and x = 3. Solving for x given f(x) is common in inverse function problems. Review solving linear equations at .
Given f(x) = x^2 and g(x) = 2x - 1, find (g ? f)(2).
9
8
3
7
First compute f(2) = 2^2 = 4, then g(4) = 2·4 - 1 = 7. Compositions always evaluate the inner function first. More detail at .
What is the domain of (g ? f)(x) if f(x) = ?(x + 1) and g(x) = 1/x?
x > -1
x ? 0
x ? -1, x ? -1
x ? -1
For g(f(x)) = 1/?(x + 1), we need x + 1 ? 0 (so x ? -1) and ?(x + 1) ? 0 (so x ? -1). Thus x > -1 actually. However, x = -1 makes the denominator zero so it's excluded. See domain of composite radicals at .
If f(x) = 3x/(x - 2), what is f(f(1))?
9/5
-9/5
5/3
3/5
First compute f(1) = 3·1/(1 - 2) = 3/(-1) = -3. Then f(-3) = 3(-3)/(-3 - 2) = -9/(-5) = 9/5. Composite evaluation can yield fractions; see more at .
Express (f ? g)(t) given f(x) = x^2 - 4 and g(x) = 2x + 3.
4t^2 + 6t - 4
4t^2 + 12t - 4
4t^2 + 12t + 5
2t^2 + 3t - 4
Compute g(t) = 2t + 3, then f(g(t)) = (2t + 3)^2 - 4 = 4t^2 + 12t + 9 - 4 = 4t^2 + 12t + 5. Composition often requires algebraic expansion. Learn more at .
What is the domain of f(x) = (x - 1)/?(x^2 - 4)?
-2 < x < 2
x > 2 or x < -2
x ? 2 or x ? -2
All real except x = ±2
The denominator ?(x^2 - 4) requires x^2 - 4 > 0 so x > 2 or x < -2. Cannot include ±2 because that makes the denominator zero. See domain of rational radicals at .
If f(x) = (2x + 1)/(x - 2), what is f?¹(4)?
7/2
5/2
3/2
9/2
Set (2x + 1)/(x - 2) = 4, so 2x + 1 = 4(x - 2) = 4x - 8, then -2x = -9 giving x = 9/2. This solves for the inverse value. For details on finding inverse functions, see .
If h(x) = f(g(x)), express h?¹(x) in terms of f?¹ and g?¹.
g(g?¹(f?¹(x)))
f(g?¹(f?¹(x)))
g?¹(f?¹(x))
f?¹(g?¹(x))
The inverse of a composition reverses the order: h?¹(x) = g?¹(f?¹(x)). You apply the inverse of the outer function first and then the inner. For more on inverses of compositions, see .
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Study Outcomes

  1. Evaluate function values -

    Through this function notation practice problems quiz, learners will accurately compute f(x) for various inputs and expressions, demonstrating proficiency in function evaluation.

  2. Determine domain and range -

    Students will determine the domain and range of functions using grade 11 function notation techniques, ensuring they can identify valid inputs and outputs.

  3. Simplify composite functions -

    Practice function notation exercises will guide students through forming and simplifying composite functions, boosting confidence with f(g(x)) challenges.

  4. Interpret function notation -

    Readers will interpret variations like f(x+h) and f^-1(x), understanding how these changes impact the graph and values of functions.

  5. Apply problem-solving strategies -

    By engaging with interactive function notation practice problems, students will apply effective strategies for solving quizzes and preparing for exams.

Cheat Sheet

  1. Defining f(x) and the Vertical Line Test -

    Function notation f(x) represents the output corresponding to input x, a concept emphasized in university-level calculus texts. The vertical line test on a graph confirms a curve is truly a function by ensuring each x-value maps to only one y-value. This quick check helps you breeze through function notation practice problems with confidence!

  2. Evaluating Functions by Substitution -

    To evaluate f(a), simply replace every x in the rule f(x) with a and simplify, for example f(x)=2x+3 gives f(2)=7. Consistent practice with diverse rule types - polynomial, rational, or radical - sharpens your substitution skills. Think "plug-and-play" to master these practice function notation exercises swiftly.

  3. Determining Domain and Range -

    The domain lists all allowable x-values, while the range lists all possible outputs f(x); start by excluding values that cause division by zero or negative radicands. Sketching a graph or using interval notation, like x≠3 for 1/(x - 3), keeps your grade 11 function notation work precise. Remember DRY: Domain first, Range second, Your graph third!

  4. Working with Composite Functions -

    Composite functions combine two rules: (f∘g)(x)=f(g(x)), so you evaluate g(x) first, then plug that result into f. Practicing with sample pairs, like f(x)=x+1 and g(x)=2x, builds fluency - (f∘g)(x)=2x+1. Visualizing machines in series (input → g → f → output) makes composite function quizzes feel like a breeze.

  5. Interpreting Transformations in Function Notation -

    Changes inside the parentheses, like f(x - h), shift the graph horizontally, while changes outside, like f(x)+k, shift it vertically. For example, f(x - 2)+3 moves f(x) right by 2 and up by 3. Spotting these "inside vs outside" cues boosts your speed on function notation exercises and builds exam-day confidence.

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