Find the value of k, such that f o g = g o f.
Example 1 :
f(x) = 3x + 2 and g(x) = 6x - k
Solution :
f o g = g o f
f[g(x)] = g[f(x)]
f[6x - k] = g[3x + 2]
3(6x - k) + 2 = 6(3x + 2) - k
18x - 3k + 2 = 18x + 12 - k
Subtract 18x from each side.
-3k + 2 = 12 - k
Add k to each side.
-2k + 2 = 12
Subtract 2 from each side.
-2k = 10
Divide each side by -2.
k = -5
Example 2 :
f(x) = 2x - k and g(x) = 4x + 5
Solution :
f o g = g o f
f[g(x)] = g[f(x)]
f[4x + 5] = g[2x - k]
2(4x + 5) - k = 4(2x - k) + 5
8x + 10 - k = 8x - 4k + 5
Subtract 18x from each side.
10 - k = -4k + 5
Add 4k to each side.
10 + 3k = 5
Subtract 10 from each side.
3k = -5
Divide each side by 3.
k = -5/3
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