Home
Class 12
MATHS
f:R->R is defined as f(x)=2x+|x| then f(...

`f:R->R` is defined as `f(x)=2x+|x|` then `f(3x)-f(-x)-4x=`

A

f(x)

B

`-f(x)`

C

`f(-x)`

D

2f(x)

Text Solution

Verified by Experts

The correct Answer is:
D
`f : R rarr R`
`f(x) = 2x + |x|`
When `x ge 0`, then f(x) = 2x + x = 3x
When `x lt 0`, then f(x) = 2x - x = x
Now, when `x ge 0`
`f(3x)-f(-x)-4x=3x-(-3x)-4x=2x=2f(x)`
Promotional Banner

Similar Questions

Explore conceptually related problems

f:R rarr R, function f(x) is defined as f(x)= 2x +|x| then f(2x)+f(-x)-f(x) = ...........

If f: R rarrR is defined by f(x) =x^(2)-3x+2 , find f(f(x)).

Let f:R to R be defined by f(x)=3x-4 . Then, f^(-1) (x) is

If f:R -> R, g:R -> R defined as f(x) = sin x and g(x) = x^2 , then find the value of (gof)(x) and (fog)(x) and also prove that gof != fog .

Let the f : R to R be defined by f(x)=2x+cos x , then f …………….

f:R to R is a function defined by f(x)= 10x -7, if g=f^(-1) then g(x)=

f and g are real functions defined by f(x)= 2x + 1 and g(x) =4x -7. If f(x) = g(x) then x = …. .