Function — Flashcards
Gujarat Board · Class 11 · Statistics
20 flashcards for Function (Gujarat Board Class 11 Statistics) to test yourself on key terms and facts. Sample: "Given f: {1, 2, 3, 4} → {5, 6, 7, 8}.
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Given f: {1, 2, 3, 4} → {5, 6, 7, 8} where f(x) = x + 4. Find f(2) and verify this is a function.
Answer
Step 1: Apply f(x) = x + 4 with x = 2 f(2) = 2 + 4 = 6 Step 2: Verify it's a function - f(1) = 5, f(2) = 6, f(3) = 7, f(4) = 8 - Each element in domain has exactly one image - All elements in domain …
For f(x) = 2x² + 1 with domain {-2, -1, 0, 1, 2}, find the range of f.
Answer
Step 1: Calculate f(x) for each domain element f(-2) = 2(-2)² + 1 = 2(4) + 1 = 9 f(-1) = 2(-1)² + 1 = 2(1) + 1 = 3 f(0) = 2(0)² + 1 = 0 + 1 = 1 f(1) = 2(1)² + 1 = 2(1) + 1 = 3 f(2) = 2(2)² + 1 = 2(4) …
Determine if f: {-2, -1, 1, 2} → {2, 5} where f(x) = x² + 1 is one-one or many-one.
Answer
Step 1: Calculate function values f(-2) = (-2)² + 1 = 4 + 1 = 5 f(-1) = (-1)² + 1 = 1 + 1 = 2 f(1) = (1)² + 1 = 1 + 1 = 2 f(2) = (2)² + 1 = 4 + 1 = 5 Step 2: Check for repeated images f(-1) = f(1) = …
For g: {1, 2, 3} → {5} where g(x) = 5, identify the type of function and find its range.
Answer
Step 1: Calculate function values g(1) = 5 g(2) = 5 g(3) = 5 Step 2: Analyze the pattern All domain elements map to the same value (5) Step 3: Classification This is a constant function because ever…
Solve: If f(x) = (2x - 4)/(x + 7), find the value of x for which f(x) = 0.
Answer
Step 1: Set up the equation f(x) = 0 (2x - 4)/(x + 7) = 0 Step 2: For a fraction to equal zero, numerator must be zero 2x - 4 = 0 2x = 4 x = 2 Step 3: Verify denominator is not zero When x = 2: x + …
Given f(x) = x² - 2x + 1 and g(x) = (x - 1)², check if f = g for domain {0, 1, 2, 3}.
Answer
Step 1: Calculate f(x) for each domain value f(0) = 0² - 2(0) + 1 = 1 f(1) = 1² - 2(1) + 1 = 0 f(2) = 2² - 2(2) + 1 = 1 f(3) = 3² - 2(3) + 1 = 4 Step 2: Calculate g(x) for each domain value g(0) = (0…
If f(x) = 1/(1 - x²) where x ∈ R - {-1, 1}, calculate f(2) - f(-2).
Answer
Step 1: Calculate f(2) f(2) = 1/(1 - 2²) = 1/(1 - 4) = 1/(-3) = -1/3 Step 2: Calculate f(-2) f(-2) = 1/(1 - (-2)²) = 1/(1 - 4) = 1/(-3) = -1/3 Step 3: Find f(2) - f(-2) f(2) - f(-2) = -1/3 - (-1/3) …
For h: A → B where A = {2, 5, 6}, B = {1, 2/3, 4/5, 11/7, 13/8} and h(x) = (2x-1)/(x+1), find the range.
Answer
Step 1: Calculate h(x) for each domain element h(2) = (2(2)-1)/(2+1) = (4-1)/(3) = 3/3 = 1 h(5) = (2(5)-1)/(5+1) = (10-1)/(6) = 9/6 = 3/2 h(6) = (2(6)-1)/(6+1) = (12-1)/(7) = 11/7 Step 2: Check which…
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