11th grade Find the inverse of a function, restrict the domain, and check by composition worksheet

Find the inverse of a function, restrict the domain, and check by composition

Grade 11 Math Worksheet

Circle the best answer, or write your answer on the line.

1. 1.

   On a worksheet, f(x) = (x + 5)/3. Pia finds the inverse as one x-term and one number. Type fractions like 1/2. What is f⁻¹(x)?
2. 2.

   In a notebook, Ren has f(x) = 6 − 2x. Write f⁻¹(x) as one x-term and one number. What is it?
3. 3.

   Tala finds the inverse of f(x) = (2x − 1)/5 in pencil, as one x-term and one number. What is f⁻¹(x)?
4. 4.

   On a puzzle card, f(x) = 9 − 3x. Zee needs f⁻¹(x) as one x-term and one number. What is it?
5. 5.

   On a worksheet, f(x) = √(x − 2) for x ≥ 2. Ari writes the rule for f⁻¹, which has the domain x ≥ 0. Type powers like x^2. What is f⁻¹(x)?
6. 6.

   In a notebook, Bo inverts f(x) = √(x + 5) for x ≥ -5. The inverse has domain x ≥ 0. What is the rule for f⁻¹(x)?
7. 7.

   Esme works in pencil with f(x) = √x + 3 for x ≥ 0. Type powers like x^2. What is f⁻¹(x) for x ≥ 3?
8. 8.

   On a puzzle card, f(x) = √x − 4 for x ≥ 0. Jun needs the rule for f⁻¹(x), for x ≥ -4. What is it?
9. 9.

   On a worksheet, f(x) = x² − 6x + 10 is a parabola. Kira keeps its right half so f has an inverse. Which domain does that?

   • x ≥ 6
   • x ≥ -3
   • x ≥ 0
   • x ≥ 3
10. 10.

    In a notebook, Luz restricts f(x) = (x + 2)² − 4 to its right half so f⁻¹ exists. Which domain is that?

    • x ≥ 2
    • x ≥ -2
    • All real numbers
    • x ≥ 0