we've got : f(x) = a-x /g(x) =2x+b Find the relashion between a and b For : G(round)F= F(round) G sry for bad eng & thanks?
回答 (2)
2015-10-24 2:52 pm
f(x) = a-x. g(x) = 2x+b. g o f = g[f(x)] = g[a-x] = 2(a-x) + b...[1].
f o g = f[g(x)] = f[2x+b] = a-(2x+b) = (a-b) - 2x...[2]. Now for g o f = f o g,
we require 2(a-x) + b = (a-b) -2x, ie., 2a + b = a-b, ie., a+2b = 0.
f o g = f[g(x)] = f[2x+b] = a-(2x+b) = (a-b) - 2x...[2]. Now for g o f = f o g,
we require 2(a-x) + b = (a-b) -2x, ie., 2a + b = a-b, ie., a+2b = 0.
2015-10-24 12:37 pm
i) As given it is likely: f(x) = a- x; and g(x) = 2x + b; As well gof= fog. Find a relation between a & b?
ii) gof(x) = g{f(x)} = g(a-x) = 2(a - x) + b = 2a - 2x + b ------------ (1)
fog(x) = f{g(x)} = f(2x + b) = a - (2x + b) = a - 2x - b -------------- (2)
iii) Equating (1) & (2): 2a - 2x + b = a - 2x - b
==> a + 2b = 0 (or) a = -2b
ii) gof(x) = g{f(x)} = g(a-x) = 2(a - x) + b = 2a - 2x + b ------------ (1)
fog(x) = f{g(x)} = f(2x + b) = a - (2x + b) = a - 2x - b -------------- (2)
iii) Equating (1) & (2): 2a - 2x + b = a - 2x - b
==> a + 2b = 0 (or) a = -2b
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