Let f:R to R be defined by f(x) = 2x + |x|,th | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Given the function $f(x) = 2x + |x|$.First,calculate $f(2x)$:$f(2x) = 2(2x) + |2x| = 4x + 2|x|$.Next,calculate $f(-x)$:$f(-x) = 2(-x) + |-x| = -2x

Vedclass · Accepted Answer

$2|x|$

Vedclass · Answer

(B) Given the function $f(x) = 2x + |x|$.First,calculate $f(2x)$:$f(2x) = 2(2x) + |2x| = 4x + 2|x|$.Next,calculate $f(-x)$:$f(-x) = 2(-x) + |-x| = -2x + |x|$.Now,substitute these into the expression $f(2x) + f(-x) - f(x)$:$= (4x + 2|x|) + (-2x + |x|) - (2x + |x|)$.$= 4x + 2|x| - 2x + |x| - 2x - |x|$.Combine the like terms:$= (4x - 2x - 2x) + (2|x| + |x| - |x|)$.$= 0x + 2|x| = 2|x|$.

Let $f:R \to R$ be defined by $f(x) = 2x + |x|$,then $f(2x) + f(-x) - f(x) = $

Similar Questions

If $A = \{x, y\}$,then the power set of $A$ is

If $n(A) = 4$,$n(B) = 3$,and $n(A \times B \times C) = 24$,then $n(C) = $

Find the cardinal number of the following set: $\{x: x \text{ is a letter of the word } 'ASSASSINATION' \}$

If $A = \{a, b\}$,$B = \{c, d\}$,$C = \{d, e\}$,then the set $\{(a, c), (a, d), (a, e), (b, c), (b, d), (b, e)\}$ is equal to:

If $f: R \to R$,then the range of the function $f(x) = \frac{x^2}{x^2 + 1}$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module