Identify the correct relationship between x and y from the given table.x -2 -1 0 1 2 y 3 4 5 6 7
Checking the pairs in the table: when x = -2, y = 3, and -2 + 5 = 3, which matches. Testing x = 2, y = 7, and 2 + 5 = 7, which also matches. So every pair in the table satisfies \(y = x + 5\).
Important Questions from Relations and Functions
Consider the following statements:
1. The relation f defined by \(f(x)= \begin{cases}x^3, & 0 \leq x \leq 2 \\ 4 x, & 2 \leq x \leq 8\end{cases}\) is a function.
2. The relation g defined by \(g(x)= \begin{cases}x^2, & 0 \leq x \leq 4 \\ 3 x, & 4 \leq x \leq 8\end{cases}\) is a function.
Which of the statements given above is/are correct?
A function satisfies \(f(x-y)=\frac{f(x)}{f(y)}\), where f(y) ≠ 0. If f(1) = 0.5, then what is f(2) + f(3) + f(4) + f(5) + f(6) equal to ?
A mapping f : A → B defined as \(f(x)=\frac{2 x+3}{3 x+5}, x \in A\) If f is to be onto, then what are A and B equal to ?
If f(x) = x(4x2 - 3), then what is f(sinθ) equal to ?
Let R be a relation on the set N of natural numbers defined by ‘nRm ⟺ n is a factor of m’. Then which one of the following is correct?
