Find the value of k, such that fog = gof
(i) f(x) = 3x + 2, g(x) = 6x - k
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Answered by
3
(i): fog = f(g(x)) = f(6x - k)
(ii): gof = g(f(x)) = g(3x + 2)
As f(x) = 3x + 2:
=> f(6x - k) = 3(6x - k) + 2
=> f(6x - k) = 18x - 3k + 2
As g(x) = 6x - k:
=> g(3x + 2) = 6(3x + 2) - k
=> g(3x + 2) = 18x + 12 - k
According to the question:
=> fog = gof
=> f(6x - k) = g(3x + 2)
=> 18x - 3k + 2 = 18x + 12 - k
=> 2 - 12 = 3k - k
=> - 10 = 2k
=> - 5 = k
Required value of k is - 5.
Answered by
4
Step-by-step explanation:
ANSWER________✍️
(i) f(x) = 3x + 2, g(x) = 6x – k
fog(x) = f(g(x)) = f(6x – k) = 3(6x – k) + 2
= 18x – 3k + 2 … (1)
gof(x) = g(f(x)) = g(3x + 2) = 6(3x + 2) – k
- = 18x + 12 – k … (2)
- 1) = (2)
- ⇒ 18x – 3k + 2 = 18x + 12 – k
- 2k = -10
- k = -5
(ii) f(x) = 2x – k, g(x) = 4x + 5
fog(x) = f(g(x)) = f(4x + 5) = 2(4x + 5) – k = 8x + 10 – k … (1)
gof(x) = g(f(x)) = g(2x – k) = 4(2x – k) + 5 = 8x – 4k + 5 ... (2)
- (1) = (2)
- ⇒ 8x + 10 – k = 8x – 4k + 5
- 3k = -5
- k = -5/3
hope this helps you
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