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

Answer Key - Grade 11 Math Worksheet - Challenge Me

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

1. 1.

   On a worksheet, f(x) = (x + 2)² − 5 for x ≥ -2. Pia finds the inverse, with domain x ≥ -5. What is f⁻¹(x)?

   • 1/((x + 2)² − 5)
   • √(x − 2) + 5
   • √(x + 5) − 2
   • -√(x + 5) − 2
   • √(x − 5) + 2
2. 2.

   In a notebook, Ren inverts f(x) = (x − 5)² + 1, kept to x ≥ 5. What is f⁻¹(x) for x ≥ 1?

   • -√(x − 1) + 5
   • 1/((x − 5)² + 1)
   • √(x + 1) − 5
   • √(x − 1) + 5
   • √(x + 5) − 1
3. 3.

   Tala works in pencil with f(x) = (x − 1)² + 3 for x ≤ 1. Which rule is f⁻¹(x)?

   • -1 − √(x + 3)
   • 1 + √(x − 3)
   • 1 − √(x − 3)
   • 1/((x − 1)² + 3)
   • -√(x + 1) − 3
4. 4.

   On a puzzle card, f(x) = (x + 4)² − 2 for x ≤ -4. Zee needs the rule for f⁻¹(x). What is it?

   • -4 − √(x + 2)
   • -√(x − 4) + 2
   • -4 + √(x + 2)
   • 4 − √(x − 2)
   • 1/((x + 4)² − 2)
5. 5.

   On a worksheet, f(x) = 3/(x − 2). Ari swaps x and y and solves for y. What is f⁻¹(x)?

   • 3/y + 2
   • 3/(x + 2)
   • (x − 2)/3
   • 3/x − 2
   • 3/x + 2
6. 6.

   Esme works in pencil to invert f(x) = 2/(x + 3). Which rule is f⁻¹(x)?

   • 2/x + 3
   • (x + 3)/2
   • 2/(x − 3)
   • 2/x − 3
   • 2/y − 3
7. 7.

   On a puzzle card, f(x) = 6/x − 2. Jun needs f⁻¹(x). What is it?

   • 6/x + 2
   • 6/(y + 2)
   • 6/(x − 2)
   • x/(-2x + 6)
   • 6/(x + 2)
8. 8.

   On a worksheet, f(x) = 2x + 6 and g(x) = (1/2)x − 3. Kira composes them to test whether g is f⁻¹. What is f(g(x))?

   x
9. 9.

   In a notebook, Luz has f(x) = 3x − 4 and g(x) = (1/3)x + 4. What is f(g(x)), with like terms combined?

   x + 8
10. 10.

    Milo checks in pencil whether g(x) = (1/4)x + 3/4 undoes f(x) = 4x − 3. What is f(g(x))?

    x