Question

It f(×) = 3×-2,g(×) = 2×+k and if f o g = g o f,then find the value of k
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Answer 1

Step-by-step explanation:

so a function

$f(x) = 3x - 2 \\ \\ g(x) = 2x + k$

Now it says,

$f(g(x)) = g(f(x)) \\ \\ 3(2x + k) - 2 = 2(3x - 2) + k \\ \\ \cancel{6x} + 3k - 2 = \cancel{6x} - 4 + k \\ \\ 2k = - 4 + 2 \\ \\ 2k = - 2 \\ \\ \implies \: k = - 1$