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.
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)?
In a notebook, Ren has f(x) = 6 − 2x. Write f⁻¹(x) as one x-term and one number. What is it?
Tala finds the inverse of f(x) = (2x − 1)/5 in pencil, as one x-term and one number. What is f⁻¹(x)?
On a puzzle card, f(x) = 9 − 3x. Zee needs f⁻¹(x) as one x-term and one number. What is it?
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)?
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)?
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?
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 ≥ 0
- x ≥ 3
- x ≥ 6
- x ≥ -3
Milo works in pencil with f(x) = x² − 2x − 4. Keeping only the left half gives an inverse. Which domain is that?
- x ≤ 1
- x ≤ -1
- x ≤ 2
- x ≤ 0
On a puzzle card, f(x) = (x + 4)² + 2. Noah keeps the left half of the parabola for an inverse. Which domain is that?
- x ≤ -4
- x ≤ 4
- All real numbers
- x ≤ 0