If f: R → R defined by f(x) = 3x – 6 and g : R → R defined by g(x) = 3x + k if fog – gof then the value of k is …
(1) – 5
(2) 5
(3) 6
(4) -6
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5
(4) – 6
f(x) = 3x – 6; g(x) = 3x + k
fog = f[g(x)]
= f(3x + k)
= 3(3x + k) – 6
= 9x + 3k – 6
gof = g[f(x)]
= g(3x – 6)
= 3(3x – 6) + k
= 9x – 18 + k
But fog = gof
9x + 3k – 6 = 9x – 18 + k
3k – k = -18 + 6
2k = -12
k = -12/2 = -6
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