If \(f(x) = x^2 \), find \(\frac {f(1.1)-f(1)}{(1.1-1)}\)
Solution and Explanation
\(f(x)=x^2\)
∴ \(\frac {f(1.1)-f(1)}{(1.1-1)}\)
= \(\frac {f(1.1)^2-f(1)^2}{(1.1-1)}\)
= \(\frac {1.21-1}{0.1}\)
= \(\frac {0.21}{0.1}\)
= \(2.1\)
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Concepts Used:
Relations and functions
A relation R from a non-empty set B is a subset of the cartesian product A × B. The subset is derived by describing a relationship between the first element and the second element of the ordered pairs in A × B.
A relation f from a set A to a set B is said to be a function if every element of set A has one and only one image in set B. In other words, no two distinct elements of B have the same pre-image.
Representation of Relation and Function
Relations and functions can be represented in different forms such as arrow representation, algebraic form, set-builder form, graphically, roster form, and tabular form. Define a function f: A = {1, 2, 3} → B = {1, 4, 9} such that f(1) = 1, f(2) = 4, f(3) = 9. Now, represent this function in different forms.
- Set-builder form - {(x, y): f(x) = y2, x ∈ A, y ∈ B}
- Roster form - {(1, 1), (2, 4), (3, 9)}
- Arrow Representation
