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25 Jun 2022, 05:45
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\(f(x)=\frac{(x-k)}{5}\) and \(g(x)= 5x + 7\). If \(f(g(x)) = g(f(x))\), what is the value of k?
A. 2
B. 4
C. 5
D. 7
E. 9
A. 2
B. 4
C. 5
D. 7
E. 9
25 Jun 2022, 15:20
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Classic question of functions that you learnt in your high school first year.
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745D25E4-A4EB-455C-9554-884AF1F8C40E.jpeg [ 320.63 KiB | Viewed 1082 times ]
26 Jun 2022, 00:38
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\(f(x)=\frac{(x−k)}{5}\) and \(g(x)=5x+7\)
\(f(g(x))\) implies substitute \(x\) in \(f(x)\) by \((5x+7)\)
\(f(g(x)) = \frac{(5x+7)-k }{ 5}\)
\(g(f(x))\) implies substitute \(x\) in \(g(x)\) by \(\frac{(x-k)}{5}\)
\(g(f(x)) = 5 \frac{(x-k)}{5} + 7 = x-k+7\)
\(f(g(x))=g(f(x))\)
=> \(\frac{(5x+7)-k }{ 5} = x-k+7\)
=> \(5x+7-k = 5x-5k+35\)
=> \(7-k = -5k+35\)
=> \(4k = 28\)
=> \(k = 7\)
Answer: D
\(f(g(x))\) implies substitute \(x\) in \(f(x)\) by \((5x+7)\)
\(f(g(x)) = \frac{(5x+7)-k }{ 5}\)
\(g(f(x))\) implies substitute \(x\) in \(g(x)\) by \(\frac{(x-k)}{5}\)
\(g(f(x)) = 5 \frac{(x-k)}{5} + 7 = x-k+7\)
\(f(g(x))=g(f(x))\)
=> \(\frac{(5x+7)-k }{ 5} = x-k+7\)
=> \(5x+7-k = 5x-5k+35\)
=> \(7-k = -5k+35\)
=> \(4k = 28\)
=> \(k = 7\)
Answer: D
