Find fog and gof , if (i)`f(x)= |x|` and `g(x)=|5x-2|`(ii) `f(x)=8x^3` and `g(x)=x^(1//3)`

Explanation

(i) `f(x) = |x| and g(x) = | 5x - 2|`
`therefore (gof) (x) = g{f(x) } = g{|x|} =|5|x| - 2|`
and `(fog)(x) = f{g(x)} = f{|5x -2|}`
`" " = || 5x - 2|| = | 5x - 2|`
(ii) `f(x) = 8x^(3) and g(x) = x^(1//3)`
`(gof)(x) = g{f(x)} = g(8x^(3))`
`" " = g (8x^(3))^(1//3) = 2x`
and `(fog)(x) = f{g(x)} = f(x^(1//3)) = 8 (x^(3))^(1//3)= 8x `