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Inverse Functions — Easy Worksheet 1
Grade 12 · MathSheets Name: ____________________ Date: __________
Solve each problem.
How to solve
To find f⁻¹(k), set f(x) = k and solve for x. To find the inverse function, write y = mx + b, swap x and y, and solve for y, giving f⁻¹(x) = x - bm.
Example
If f(x) = 3x + 2, find f⁻¹(-7).
Answer: -3
Not quite. The answer is
💡 f⁻¹(8) is the input x that gives f(x) = 8. Solve 2x + 4 = 8. Subtract 4 from both sides: 2x = 4. Divide both sides by 2: x = 2. Check: f(2) = 2(2) + 4 = 4 + 4 = 8. So f⁻¹(8) = 2.
✓ Correct!
Not quite. The answer is
💡 f⁻¹(8) is the input x that gives f(x) = 8. Solve 2x + 4 = 8. Subtract 4 from both sides: 2x = 4. Divide both sides by 2: x = 2. Check: f(2) = 2(2) + 4 = 4 + 4 = 8. So f⁻¹(8) = 2.
💡 How to solve: Inverse Functions
To find f⁻¹(k), set f(x) = k and solve for x. To find the inverse function, write y = mx + b, swap x and y, and solve for y, giving f⁻¹(x) = x - bm.
Try a similar one
If f(x) = x, find f⁻¹(1).
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 f⁻¹(−7) is the input x that gives f(x) = −7. Solve −2x − 3 = −7. Add 3 to both sides: −2x = −4. Divide both sides by −2: x = 2. Check: f(2) = −2(2) − 3 = −4 − 3 = −7. So f⁻¹(−7) = 2.
✓ Correct!
Not quite. The answer is
💡 f⁻¹(−7) is the input x that gives f(x) = −7. Solve −2x − 3 = −7. Add 3 to both sides: −2x = −4. Divide both sides by −2: x = 2. Check: f(2) = −2(2) − 3 = −4 − 3 = −7. So f⁻¹(−7) = 2.
💡 How to solve: Inverse Functions
To find f⁻¹(k), set f(x) = k and solve for x. To find the inverse function, write y = mx + b, swap x and y, and solve for y, giving f⁻¹(x) = x - bm.
Try a similar one
If f(x) = -2x - 1, find f⁻¹(-7).
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 f⁻¹(−7) is the input x that gives f(x) = −7. Solve −4x − 3 = −7. Add 3 to both sides: −4x = −4. Divide both sides by −4: x = 1. Check: f(1) = −4(1) − 3 = −4 − 3 = −7. So f⁻¹(−7) = 1.
✓ Correct!
Not quite. The answer is
💡 f⁻¹(−7) is the input x that gives f(x) = −7. Solve −4x − 3 = −7. Add 3 to both sides: −4x = −4. Divide both sides by −4: x = 1. Check: f(1) = −4(1) − 3 = −4 − 3 = −7. So f⁻¹(−7) = 1.
💡 How to solve: Inverse Functions
To find f⁻¹(k), set f(x) = k and solve for x. To find the inverse function, write y = mx + b, swap x and y, and solve for y, giving f⁻¹(x) = x - bm.
Try a similar one
If f(x) = -4x - 3, find f⁻¹(5).
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 f⁻¹(4) is the input x that gives f(x) = 4. Solve −3x + 1 = 4. Subtract 1 from both sides: −3x = 3. Divide both sides by −3: x = −1. Check: f(−1) = −3(−1) + 1 = 3 + 1 = 4. So f⁻¹(4) = −1.
✓ Correct!
Not quite. The answer is
💡 f⁻¹(4) is the input x that gives f(x) = 4. Solve −3x + 1 = 4. Subtract 1 from both sides: −3x = 3. Divide both sides by −3: x = −1. Check: f(−1) = −3(−1) + 1 = 3 + 1 = 4. So f⁻¹(4) = −1.
💡 How to solve: Inverse Functions
To find f⁻¹(k), set f(x) = k and solve for x. To find the inverse function, write y = mx + b, swap x and y, and solve for y, giving f⁻¹(x) = x - bm.
Try a similar one
If f(x) = 2x - 2, find f⁻¹(-4).
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 f⁻¹(−1) is the input x that gives f(x) = −1. Solve −x + 3 = −1. Subtract 3 from both sides: −x = −4. Divide both sides by −1: x = 4. Check: f(4) = −4 + 3 = −1. So f⁻¹(−1) = 4.
✓ Correct!
Not quite. The answer is
💡 f⁻¹(−1) is the input x that gives f(x) = −1. Solve −x + 3 = −1. Subtract 3 from both sides: −x = −4. Divide both sides by −1: x = 4. Check: f(4) = −4 + 3 = −1. So f⁻¹(−1) = 4.
💡 How to solve: Inverse Functions
To find f⁻¹(k), set f(x) = k and solve for x. To find the inverse function, write y = mx + b, swap x and y, and solve for y, giving f⁻¹(x) = x - bm.
Try a similar one
If f(x) = -4x + 1, find f⁻¹(1).
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 f⁻¹(−1) is the input x that gives f(x) = −1. Solve 4x − 1 = −1. Add 1 to both sides: 4x = 0. Divide both sides by 4: x = 0. Check: f(0) = 4(0) − 1 = 0 − 1 = −1. So f⁻¹(−1) = 0.
✓ Correct!
Not quite. The answer is
💡 f⁻¹(−1) is the input x that gives f(x) = −1. Solve 4x − 1 = −1. Add 1 to both sides: 4x = 0. Divide both sides by 4: x = 0. Check: f(0) = 4(0) − 1 = 0 − 1 = −1. So f⁻¹(−1) = 0.
💡 How to solve: Inverse Functions
To find f⁻¹(k), set f(x) = k and solve for x. To find the inverse function, write y = mx + b, swap x and y, and solve for y, giving f⁻¹(x) = x - bm.
Try a similar one
If f(x) = -x - 2, find f⁻¹(-1).
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Write y = 3x + 1. Swap x and y: x = 3y + 1. Subtract 1 from both sides: x − 1 = 3y. Divide both sides by 3: y = x − 13. So f⁻¹(x) = x − 13.
✓ Correct!
Not quite. The answer is
💡 Write y = 3x + 1. Swap x and y: x = 3y + 1. Subtract 1 from both sides: x − 1 = 3y. Divide both sides by 3: y = x − 13. So f⁻¹(x) = x − 13.
💡 How to solve: Inverse Functions
To find f⁻¹(k), set f(x) = k and solve for x. To find the inverse function, write y = mx + b, swap x and y, and solve for y, giving f⁻¹(x) = x - bm.
Try a similar one
If f(x) = x + 4, find f⁻¹(7).
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Write y = 2x + 2. Swap x and y: x = 2y + 2. Subtract 2 from both sides: x − 2 = 2y. Divide both sides by 2: y = x − 22. So f⁻¹(x) = x − 22.
✓ Correct!
Not quite. The answer is
💡 Write y = 2x + 2. Swap x and y: x = 2y + 2. Subtract 2 from both sides: x − 2 = 2y. Divide both sides by 2: y = x − 22. So f⁻¹(x) = x − 22.
💡 How to solve: Inverse Functions
To find f⁻¹(k), set f(x) = k and solve for x. To find the inverse function, write y = mx + b, swap x and y, and solve for y, giving f⁻¹(x) = x - bm.
Try a similar one
If f(x) = x + 1, find f⁻¹(5).
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
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Inverse Functions — Easy Worksheet 1
Solve each problem.