# composite functions

• Apr 22nd 2007, 11:45 AM
sillyhacker
composite functions
Hello people,

i need a bit of help with these proofs, its one of those things were i can't sport what to do with the thing next.

1) f(x)=2x +lnx, g(x) = e^2x, prove that gf(x)=4e^4x

2) (cosec x)^4 - (cot x)^4 = (cosec x )^2 + (cot x)^2

3)

P= (2800ae^0.2t)/(1 +ae^0.2t) a=0.12

show that p = 336/(0.12 + e^-0.2t)
• Apr 22nd 2007, 11:52 AM
CaptainBlack
Quote:

Originally Posted by sillyhacker
i need a bit of help with these proofs, its one of those things were i can't sport what to do with the thing next.

1) f(x)=2x +lnx, g(x) = e^2x, prove that gf(x)=4e^4x

gf(x) = g(f(x) = e^2(f(x)) = e^{4x + 2 ln(x)) = e^{4x} e^{2ln(x)}

.............. = e^{4x} [e^{ln(x)}]^2 = e^{4x} x^2

(since e^ln(x) = x).

RonL
• Apr 22nd 2007, 11:58 AM
Jhevon
Quote:

Originally Posted by sillyhacker
2) (cosec x)^4 - (cot x)^4 = (cosec x )^2 + (cot x)^2

Here's (2)
• Apr 22nd 2007, 12:08 PM
Jhevon
Quote:

Originally Posted by sillyhacker
3)

P= (2800ae^0.2t)/(1 +ae^0.2t) a=0.12

show that p = 336/(0.12 + e^-0.2t)

P = (2800ae^0.2t)/(1 +ae^0.2t) .............................. plug in a = 0.12
=> P = [2800(0.12)e^(0.2t)]/[1 + 0.12e^(0.2t)] ..........now simplify
=> P = [336e^(0.2t)]/[1 + 0.12e^(0.2t)]
=> P = 336/{e^(-0.2t)[1 + 0.12e^(0.2t)]}
=> P = 336/[0.12e^(0.2t) * e^(-0.2t) + e^(-0.2t)]
=> P = 336/(0.12 + e^-0.2t)
• Apr 22nd 2007, 12:12 PM
sillyhacker