Algebra Practice Problems
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Questions and Answers

What is the expression obtained when finding (f-g)(x) if f(x) = 2x - 4 and g(x) = x - 2?

  • x + 6
  • x + 2
  • x - 2
  • x - 4 (correct)

What is the result of finding (f+h)(x) where f(x) = 2x - 4 and h(x) = x - 2?

  • 3x + 2
  • 3x - 6 (correct)
  • x - 6
  • 2x - 2

What is (f.g)(x) when f(x) = 1 and g(x) = √x?

  • x²
  • 2x
  • √x (correct)
  • x

What is the simplified result of (f/h)(x) if f(x) = 1 and h(x) = √x?

<p>1 (C)</p> Signup and view all the answers

If f(x) = x² + 3 and h(x) = x - 3, what is fo h(2)?

<p>4 (B)</p> Signup and view all the answers

Given f(x) = x + 2 and g(x) = 2x + 4, what is (fog)(x)?

<p>6x + 2 (A)</p> Signup and view all the answers

What is the result of (f-h)(x) where f(x) = 2x - 4 and h(x) = x - 2?

<p>x - 4 (A)</p> Signup and view all the answers

What is the expression found for (f+h)(x) if f(x) = 1 and g(x) = √x?

<p>√x + 1 (C)</p> Signup and view all the answers

What is F(-1)?

<p>-5 (B)</p> Signup and view all the answers

What is F(x + 2)?

<p>x - 2 (C)</p> Signup and view all the answers

Given f(x) = x - 2 and g(x) = 3x + 7, what is (f + g)(x)?

<p>4x + 5 (C)</p> Signup and view all the answers

If f(x) = 2x + 2 and h(x) = 3x, find (f - h)(x).

<p>1 + x (B)</p> Signup and view all the answers

If v(x) = 2x - 7 and g(x) = x + 3, find (v + g)(x).

<p>3x - 4 (C)</p> Signup and view all the answers

If f(x) = x² + 2x + 4 and p(x) = x + 2x - 8, find (f - p)(x).

<p>x² + x - 12 (C)</p> Signup and view all the answers

If f(x) = x + 3 and p(x) = 2x - 7, find (f . p)(x).

<p>2x² - x - 21 (A)</p> Signup and view all the answers

What is (f . h)(x) if f(x) = 2x - 4 and h(x) = x - 2?

<p>x - 4 (B)</p> Signup and view all the answers

What is (f - h)(x) given f(x) = 2x - 4 and h(x) = x - 2?

<p>x (A)</p> Signup and view all the answers

What is (f + h)(x) if f(x) = 2x - 4 and h(x) = x - 2?

<p>3x - 6 (A)</p> Signup and view all the answers

What is (f / h)(x) given f(x) = 2x - 4 and h(x) = x - 2?

<p>2 (C)</p> Signup and view all the answers

What is (f o g)(x) if f(x) = x + 2 and g(x) = 2x + 4?

<p>6x + 2 (A)</p> Signup and view all the answers

What is (g o f)(x) for f(x) = x + 2 and g(x) = 2x + 4?

<p>2x - 6 (A)</p> Signup and view all the answers

What is (g o g)(x) for g(x) = 2x + 4?

<p>8 + 2x (B)</p> Signup and view all the answers

What is (f o f)(x) for f(x) = x + 2?

<p>2x + 4 (B)</p> Signup and view all the answers

If f(x) = x² + 3 and h(x) = x - 3, what is fo h(2)?

<p>4 (C)</p> Signup and view all the answers

Study Notes

Functions and Operations

  • Functions can be combined through various operations such as addition, subtraction, multiplication, and division.
  • For composite functions, the notation (f o g)(x) indicates that function g is applied first, and then function f is applied to the result.

Algebra Practice Questions

  • Various problems require identifying the correct outcomes for defined functions.
  • The range of functions includes linear functions, quadratic functions, and polynomials.

Function Evaluations

  • Given specific functions, evaluations and simplifications should lead to precise results.

Sample Function Operations

  • Addition Example: Given f(x) = 2x - 4 and g(x) = x - 2, (f + g)(x) = 3x - 6 and respectively simplifies whether the terms combine appropriately.
  • Subtraction Example: For (f - g)(x), this can yield direct results reflecting differences in the functions.
  • Multiplication Example: (f g)(x) calculates the product and highlights how multiplication of functions operates in relation to their components.
  • Division Example: Determining (f/g)(x) gives insight into how functions relate as quotients.

Function Compositions

  • Composition functions such as (f o g)(x) result in new functions that highlight relationships between f and g.
  • The order of composition significantly impacts the outcome; (g o f)(x) may differ in value from (f o g)(x).

Example Outcomes

  • Specific outcomes from the practice problems showcase different results based on operations:
    • Example: (f + g)(2) for f(x) and g(x) defined above can yield 6.
    • Composite results can lead to complex simplified forms, illustrating the depth of function relationships.

Algebraic Identities

  • Certain combinations yield unique identities:
    • For instance, (f + g) can yield either a linear or a quadratic depending on the base functions involved.

Function Outcomes

  • Recognizable patterns emerge in functions, such as repeating forms in domains defined by the same or similar bases.
  • Simplified calculations and patterns help clarify principles governing function operations.

Problem-Solving Approach

  • When finding functions, crucially check combinations and order to ensure accurate calculations.
  • Review each function definition before applying operations to maintain clarity and accuracy in outcomes.

Functions and Operations

  • Functions can be combined through various operations such as addition, subtraction, multiplication, and division.
  • For composite functions, the notation (f o g)(x) indicates that function g is applied first, and then function f is applied to the result.

Algebra Practice Questions

  • Various problems require identifying the correct outcomes for defined functions.
  • The range of functions includes linear functions, quadratic functions, and polynomials.

Function Evaluations

  • Given specific functions, evaluations and simplifications should lead to precise results.

Sample Function Operations

  • Addition Example: Given f(x) = 2x - 4 and g(x) = x - 2, (f + g)(x) = 3x - 6 and respectively simplifies whether the terms combine appropriately.
  • Subtraction Example: For (f - g)(x), this can yield direct results reflecting differences in the functions.
  • Multiplication Example: (f g)(x) calculates the product and highlights how multiplication of functions operates in relation to their components.
  • Division Example: Determining (f/g)(x) gives insight into how functions relate as quotients.

Function Compositions

  • Composition functions such as (f o g)(x) result in new functions that highlight relationships between f and g.
  • The order of composition significantly impacts the outcome; (g o f)(x) may differ in value from (f o g)(x).

Example Outcomes

  • Specific outcomes from the practice problems showcase different results based on operations:
    • Example: (f + g)(2) for f(x) and g(x) defined above can yield 6.
    • Composite results can lead to complex simplified forms, illustrating the depth of function relationships.

Algebraic Identities

  • Certain combinations yield unique identities:
    • For instance, (f + g) can yield either a linear or a quadratic depending on the base functions involved.

Function Outcomes

  • Recognizable patterns emerge in functions, such as repeating forms in domains defined by the same or similar bases.
  • Simplified calculations and patterns help clarify principles governing function operations.

Problem-Solving Approach

  • When finding functions, crucially check combinations and order to ensure accurate calculations.
  • Review each function definition before applying operations to maintain clarity and accuracy in outcomes.

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Test your algebra skills with these practice problems focused on functions and operations. Each question presents a scenario requiring you to choose the correct answer from multiple choices. Sharpen your understanding of algebraic functions and their combinations!

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