If $ f(x) = 2-2x^2,$ find $\frac {f(3,8)-f(4)} {3.8-4} $,
- 1.56
- 156
- 15.6
- 0.156
The Correct Option is C
Solution and Explanation
$\therefore\, \frac{f\left(3.8\right)-f\left(4\right)}{3.8-4}=\frac{2\left(3.8 \right)^{2}-2\left(4\right)^{2}}{3.8-4}$
$=\frac{2\left[\left(3.8\right)^{2}-\left(4\right)^{2}\right]}{3.8-4}$
$\quad \quad \quad =\frac{2\left(3.8-4\right)\left(3.8+4\right)}{3.8}=2\left(7.8\right)=15.6$
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Concepts Used:
Functions
A function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. Let A & B be any two non-empty sets, mapping from A to B will be a function only when every element in set A has one end only one image in set B.
Kinds of Functions
The different types of functions are -
One to One Function: When elements of set A have a separate component of set B, we can determine that it is a one-to-one function. Besides, you can also call it injective.
Many to One Function: As the name suggests, here more than two elements in set A are mapped with one element in set B.
Moreover, if it happens that all the elements in set B have pre-images in set A, it is called an onto function or surjective function.
Also, if a function is both one-to-one and onto function, it is known as a bijective. This means, that all the elements of A are mapped with separate elements in B, and A holds a pre-image of elements of B.
Read More: Relations and Functions