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April 16, 2014

April 16, 2014

Posted by **Shreya** on Thursday, September 27, 2012 at 10:27pm.

If f(x) = 2x+1

find

A. f o f(x)

f(f(x)) = f(2x+1)

f(2x+1) = 2(2x+1)

f(f(x)) = 4x +2

B. f o f o f o f(x)

^ I dont get how to solve this one

C. f o f o f o f o f ...o f(x) n functions of f

^ I also dont get how to solve this one

given f(x) = ax+b and g(x) = cx+d and

f o g(x) = g o f(x), what is the relationship between a,b,c,d?

- Pre-Calculus -
**Steve**, Thursday, September 27, 2012 at 11:32pmf(x) = 2x+1

f(f) = 2f+1 = 2(2x+1)+1 = 4x+3

f(f(f)) = 2(4x+3)+1 = 8x + 7

f(f(f(f(x)))) = 2(8x+7)+1 = 16x + 15

f^{n}(x) = 2^n * (x+1) - 1

f(g) = ag+b = a(cx+d)

g(f) = cf+d = c(ax+b)

so, if f(g) = g(f)

acx + ad = acx + bc

ad = bc

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