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Function Composition — Easy Worksheet 1
Grade 11 · MathSheets Name: ____________________ Date: __________
Evaluate each composed function.
How to solve
Work from the inside out. For f(g(k)), first find g(k), then put that result into f. For g(f(k)), find f(k) first, then put that result into g.
Example
If f(x) = x - 2 and g(x) = 2x, find f(g(-2)).
Answer: -6
Not quite. The answer is
💡 Work from the inside out. First find the inside function: g(−5) = −5. Then put −5 into f: f(−5) = −5 − 1 = −6. So f(g(−5)) = −6.
✓ Correct!
Not quite. The answer is
💡 Work from the inside out. First find the inside function: g(−5) = −5. Then put −5 into f: f(−5) = −5 − 1 = −6. So f(g(−5)) = −6.
💡 How to solve: Function Composition
Work from the inside out. For f(g(k)), first find g(k), then put that result into f. For g(f(k)), find f(k) first, then put that result into g.
Try a similar one
If f(x) = x + 3 and g(x) = x, find f(g(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
💡 Work from the inside out. First find the inside function: f(−2) = 2(−2) + 1 = −4 + 1 = −3. Then put −3 into g: g(−3) = −3 − 4 = −7. So g(f(−2)) = −7.
✓ Correct!
Not quite. The answer is
💡 Work from the inside out. First find the inside function: f(−2) = 2(−2) + 1 = −4 + 1 = −3. Then put −3 into g: g(−3) = −3 − 4 = −7. So g(f(−2)) = −7.
💡 How to solve: Function Composition
Work from the inside out. For f(g(k)), first find g(k), then put that result into f. For g(f(k)), find f(k) first, then put that result into g.
Try a similar one
If f(x) = 2x + 1 and g(x) = x, find f(g(-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
💡 Work from the inside out. First find the inside function: g(2) = 2 − 2 = 0. Then put 0 into f: f(0) = 2(0) + 3 = 3. So f(g(2)) = 3.
✓ Correct!
Not quite. The answer is
💡 Work from the inside out. First find the inside function: g(2) = 2 − 2 = 0. Then put 0 into f: f(0) = 2(0) + 3 = 3. So f(g(2)) = 3.
💡 How to solve: Function Composition
Work from the inside out. For f(g(k)), first find g(k), then put that result into f. For g(f(k)), find f(k) first, then put that result into g.
Try a similar one
If f(x) = x - 1 and g(x) = x, find f(g(-2)).
✓ 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
💡 Work from the inside out. First find the inside function: f(0) = 0 + 3 = 3. Then put 3 into g: g(3) = 2(3) − 1 = 6 − 1 = 5. So g(f(0)) = 5.
✓ Correct!
Not quite. The answer is
💡 Work from the inside out. First find the inside function: f(0) = 0 + 3 = 3. Then put 3 into g: g(3) = 2(3) − 1 = 6 − 1 = 5. So g(f(0)) = 5.
💡 How to solve: Function Composition
Work from the inside out. For f(g(k)), first find g(k), then put that result into f. For g(f(k)), find f(k) first, then put that result into g.
Try a similar one
If f(x) = x + 4 and g(x) = x + 4, find f(g(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
💡 Work from the inside out. First find the inside function: g(1) = 1 + 2 = 3. Then put 3 into f: f(3) = 3 + 2 = 5. So f(g(1)) = 5.
✓ Correct!
Not quite. The answer is
💡 Work from the inside out. First find the inside function: g(1) = 1 + 2 = 3. Then put 3 into f: f(3) = 3 + 2 = 5. So f(g(1)) = 5.
💡 How to solve: Function Composition
Work from the inside out. For f(g(k)), first find g(k), then put that result into f. For g(f(k)), find f(k) first, then put that result into g.
Try a similar one
If f(x) = 2x - 4 and g(x) = x - 2, find f(g(-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
💡 Work from the inside out. First find the inside function: f(−5) = −5 − 3 = −8. Then put −8 into g: g(−8) = −8 + 3 = −5. So g(f(−5)) = −5.
✓ Correct!
Not quite. The answer is
💡 Work from the inside out. First find the inside function: f(−5) = −5 − 3 = −8. Then put −8 into g: g(−8) = −8 + 3 = −5. So g(f(−5)) = −5.
💡 How to solve: Function Composition
Work from the inside out. For f(g(k)), first find g(k), then put that result into f. For g(f(k)), find f(k) first, then put that result into g.
Try a similar one
If f(x) = x + 4 and g(x) = x - 3, find f(g(-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
💡 Work from the inside out. First find the inside function: g(−2) = −2 + 4 = 2. Then put 2 into f: f(2) = 2(2) + 3 = 4 + 3 = 7. So f(g(−2)) = 7.
✓ Correct!
Not quite. The answer is
💡 Work from the inside out. First find the inside function: g(−2) = −2 + 4 = 2. Then put 2 into f: f(2) = 2(2) + 3 = 4 + 3 = 7. So f(g(−2)) = 7.
💡 How to solve: Function Composition
Work from the inside out. For f(g(k)), first find g(k), then put that result into f. For g(f(k)), find f(k) first, then put that result into g.
Try a similar one
If f(x) = x - 2 and g(x) = 2x - 3, find f(g(2)).
✓ 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
💡 Work from the inside out. First find the inside function: f(5) = 2(5) − 4 = 10 − 4 = 6. Then put 6 into g: g(6) = 6 + 2 = 8. So g(f(5)) = 8.
✓ Correct!
Not quite. The answer is
💡 Work from the inside out. First find the inside function: f(5) = 2(5) − 4 = 10 − 4 = 6. Then put 6 into g: g(6) = 6 + 2 = 8. So g(f(5)) = 8.
💡 How to solve: Function Composition
Work from the inside out. For f(g(k)), first find g(k), then put that result into f. For g(f(k)), find f(k) first, then put that result into g.
Try a similar one
If f(x) = 2x + 1 and g(x) = 2x - 4, find f(g(-1)).
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
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Function Composition — Easy Worksheet 1
Evaluate each composed function.