If f be a greatest integer function and g be an absolute value functio

1.	If f be a greatest integer function and g be an absolute value function, find the value of(f o g)\((\frac{-3}{2})\)+(g o f)\((\frac{4}{3})\).
Answer» To find: (f o g)\((\frac{-3}{2})\)+(g o f)\((\frac{4}{3})\). Formula used: (i) f o g = f(g(x)) (ii) g o f = g(f(x)) Given: (i) f is a greatest integer function (ii) g is an absolute value function f(x) = [x] (greatest integer function) g(x) = (absolute value function) \(f(\frac{4}{3})=[\frac{4}{3}]=1.....(i)\) \(g(\frac{-3}{2})=[\frac{-3}{2}]=1.5......(ii)\) Now, for (f o g)\((\frac{-3}{2})\)+(g o f)\((\frac{4}{3})\). Substituting values from (i) and (ii) \(\Rightarrow f(1.5)+g(1)\) ⇒ [1.5] +[1] ⇒ 1 + 1 = 2

If f be a greatest integer function and g be an absolute value function, find the value of(f o g)\((\frac{-3}{2})\)+(g o f)\((\frac{4}{3})\).

Answer»

To find: (f o g)\((\frac{-3}{2})\)+(g o f)\((\frac{4}{3})\).

Formula used: (i) f o g = f(g(x))

(ii) g o f = g(f(x))

Given: (i) f is a greatest integer function

(ii) g is an absolute value function

f(x) = [x] (greatest integer function)

g(x) = (absolute value function)

\(f(\frac{4}{3})=[\frac{4}{3}]=1.....(i)\)

\(g(\frac{-3}{2})=[\frac{-3}{2}]=1.5......(ii)\)

Now, for (f o g)\((\frac{-3}{2})\)+(g o f)\((\frac{4}{3})\).

Substituting values from (i) and (ii)

\(\Rightarrow f(1.5)+g(1)\)

⇒ [1.5] +[1]

⇒ 1 + 1 = 2