f(x)=x-4, 8 g(x) =x², h(x) =3x-5 then show that (fog)oh = fo(goh)
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Answer:
Step-by-step explanation:
fog = f [ g(x) ]
= f (x²)
= x² - 4
(fog) oh = fog [ h(x) ]
= fog ( 3x - 5 )
= (3x -5)² - 4
= 9x² -30x +25 - 4
= 9x² - 30x + 21 ............(1)
goh = g [h(x)]
= g ( 3x - 5)
= (3x - 5)²
= 9x² -30 x + 25
fo (g0h) = f [goh(x) ]
= f ( 9x² -30x + 25)
= 9x² - 30x + 25 - 4
= 9x² - 30x + 21 .........(2)
(1) = (2)
∴ (fog)oh = fo(goh)
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