Function
Gujarat Board · Class 11 · Statistics
Flashcards for Function — Gujarat Board Class 11 Statistics. Quick Q&A cards covering key concepts, definitions, and formulas.
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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Function covers several key topics that are frequently asked in Gujarat Board Class 11 board exams. Focus on the core concepts listed on this page and practise related questions to build confidence.
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