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Find fog and gof , if (i)f(x)= |x| and ...

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)`

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(i)Here, `f(x) = |x|,g(x) = |5x-2|`
`:. fog = f(g(x)) = f(|5x-2|) = ||5x-2|| =|5x-2|`
`gof = g(f(x)) = g(|x|) = |5|x|-2|`

(ii)Here, `f(x) = 8x^3,g(x) = x^(1/3)`
`:. fog = f(g(x)) = f(x^(1/3)) = (8(x^(1/3))^3) =8x`
`gof = g(f(x)) = g(8x^3) = (8x^3)^(1/3) = 2x`

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