Let \(f(x)\)={-\(5,x≤0 x-5,x>0\) and \(g(x)=If(x)+2f(IxI)\).Then \(g(-2)\) will be
\(-15\)
\(1\)
\(0\)
\(1\)
\(-11\)
The Correct Option is
Solution and Explanation
Given that
\(f(x)\)={\(−5,x−5,x≤0x>0\)
\(g(x)=f(x)+2f(∣x∣)\)
now \(g(−2) \) can be found by
Step 1: Since 2≤0, we use the first part of the definition of \(f(x),\) which gives us \(f(−2)=−5\).
Step 2: Since \(∣−2∣=2\) and \(2>0,\) we use the second part of the definition of f(x), which gives us \(f(∣−2∣)=∣2∣−5=2−5=−3\).
Step 3: Using the formula \(g(x)=f(x)+2f(∣x∣)\), we have:\( g(−2)=f(−2)+2f(∣−2∣)=(−5)+2(−3)=−5−6=−11.\)
Therefore, the value of \(g(−2)\text{is } -11\). (_Ans.)
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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
