Question

If f(x) =[x] and g(x) =|x|. Find fog(1/2)-gof(1/2)​

Answer 1

SOLUTION

GIVEN

f(x) = [x] and g(x) = |x|

TO DETERMINE

The value of

$\displaystyle \sf{f \circ g \bigg( \frac{1}{2} \bigg) - g\circ f \bigg( \frac{1}{2} \bigg)}$

EVALUATION

Here it is given that f(x) = [x] and g(x) = |x|

Now

$\displaystyle \sf{f \circ g \bigg( \frac{1}{2} \bigg) }$

$\displaystyle \sf{ = f \bigg(g \bigg( \frac{1}{2} \bigg) \:\bigg) }$

$\displaystyle \sf{ = f \bigg( \frac{1}{2} \bigg) }$

$\displaystyle \sf{ = 0 }$

Again

$\displaystyle \sf{g\circ f \bigg( \frac{1}{2} \bigg)}$

$\displaystyle \sf{ = g\bigg(f \bigg( \frac{1}{2} \bigg) \:\bigg) }$

$\displaystyle \sf{ = g(0) }$

= 0

Thus we get

$\displaystyle \sf{ = 0 - 0}$

$= 0$

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

1. 1. If x=u^2-v^2,y=2uv find the jacobian of x, y with respect to u and v

https://brainly.in/question/34361788

2. given u=yzx , v= zxy, w =xyz then the value of d(u,v,w)/d(x,y,z) is (a) 0 (b) 1 (c) 2 (d) 4

https://brainly.in/question/34435016