Find the inverse of a function, restrict the domain, and check by composition
Grade 11 Math Worksheet - Building Confidence
Circle the best answer, or write your answer on the line.
On a worksheet, f(x) = 3x + 6: f multiplies by 3, then adds 6. Pia writes f⁻¹(x) with one x-term and one number. What is f⁻¹(x)?
In a notebook, Ren has f(x) = 4x − 8, which multiplies by 4, then subtracts 8. Type one x-term and one number. What is f⁻¹(x)?
On a puzzle card, f(x) = 5x − 15; f multiplies by 5, then subtracts 15. Zee needs f⁻¹(x) as one x-term and one number. What is it?
On a worksheet, f(x) = x² + 3 for x ≥ 0. Ari wants the input that gives 52. What is f⁻¹(52)?
In a notebook, Bo has f(x) = x² − 5, with x ≥ 0. What is f⁻¹(76)?
Esme works in pencil with f(x) = (x − 2)² for x ≥ 2. What is f⁻¹(25)?
On a puzzle card, f(x) = (x + 3)² for x ≥ -3. Jun needs f⁻¹(64). What is it?
On a worksheet, f(x) = 3x − 4 and g(x) = (x + 4)/3. Kira tests whether g undoes f, starting with x = 5. What is g(f(5))?
In a notebook, Luz checks f(x) = 2x + 7 against g(x) = x/2 − 7 at x = 3. What is g(f(3))?
Milo works in pencil: f(x) = 4x + 1 and g(x) = (x − 1)/4. To test g as the inverse, what is g(f(6))?