Penjelasan dengan langkah-langkah:

f⁻¹o g⁻¹ o h⁻¹ (x) =

i) f⁻¹ [ g⁻¹ {h⁻¹ }](x)

ii) (hogof)⁻¹(x)

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cara 1) f⁻¹o g⁻¹ o h⁻¹ (x) = f⁻¹ [ g⁻¹ {h⁻¹ }](x)

f(x) = 4x, --> f⁻¹ (x) = 1/4 x

g(x) = 9x + 2 -->g⁻¹ (x)= 1/9 (x - 2)

h(x) = 9 - x. --> h⁻¹ = x + 9

f⁻¹o g⁻¹ o h⁻¹ (x) =

= f⁻¹ [ g⁻¹ {h⁻¹ }](x)

= f⁻¹ [ g⁻¹ {x + 9)}

= f⁻¹ [ 1/9 (x + 9 - 2)]

= f⁻¹ [ 1/9 (x + 7)}

= 1/4 [ 1/9 (x + 7 )]

= 1/36 (x + 7)

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cara ii) f⁻¹o g⁻¹ o h⁻¹ (x) = (hogof)⁻¹(x)

(h o g o f) (x) =

= h { g { f(x)}]

= h { g (4x)}

= h (9(4x) + 2)

= h (36 x + 2)

= 9 - (36 x+2)

= 7 - 36 x

(h o g o f) (x) = 7 - 36 x

(h o g o f)⁻¹ (x) = 1/36 (x + 7)

f⁻¹o g⁻¹ o h⁻¹ (x) = (h o g o f)⁻¹(x) = 1/36 (x + 7)