The problem states the mapping is X 2x2 - x + 3, and asks to find the value of a. However, the variable a is not present in the given mapping. This indicates a likely typo in the question.

b) The problem states the mapping is X 2x^2 - x + 3, and asks to find the value of a. However, the variable a is not present in the given mapping. This indicates a likely typo in the question. A common interpretation in such cases is that one of the coefficients in the quadratic expression was intended to be a. Step 1: Assume the mapping form. We will assume that the coefficient of x^2 was intended to be a, making the mapping f(x) = ax^2 - x + 3. Step 2: Use the first given condition to find a. We are given that the image of 1 is 4, which means f(1) = 4. Substitute x=1 into our assumed mapping: f(1) = a(1)^2 - (1) + 3 4 = a - 1 + 3 4 = a + 2 Subtract 2 from both sides to solve for a: a = 4 - 2 a = 2 Step 3: Verify the value of a using the second condition. We are given that the image of 2 is 9, which means f(2) = 9. Substitute x=2 and the calculated value a=2 into our assumed mapping: f(2) = 2(2)^2 - (2) + 3 f(2) = 2(4) - 2 + 3 f(2) = 8 - 2 + 3 f(2) = 6 + 3 f(2) = 9 This matches the given condition, confirming our value of a under the stated assumption. The value of a is 2. That's 2 down. 3 left today — send the next one.