Finding gof(x) and foh(x) with exponential and logarithm functions

[DJ-Smiles]

Homework Statement

Determine each of the following composite functions:
a) gof(x)
b)foh(x)

Homework Equations

Where f(x)=e^(3x+2) [e is the exponential function]
g(x)= ln(4x+1)
h(x)= 1/(2x-1)

The Attempt at a Solution

So I have found an answer, I am just unsure if I am correct though. This is what I did:

a) gof(x)=g(f(x))
= ln(4(f(x)+1)
=ln(4e^(3x+2)+1)
= ln4e^(3x+2)+ln1
=(3x+2)*4*lne+ln1
= 4(3x+2)+ln1
=12x+8+ln1
=12x+8

b)foh(x)=f(h(x))
=e^(3(h(x))+2)
=e^(3(1/(2x-1))+2)
=e^(3/(2x-1))+2)Is this the correct working out and answers?

 

[ehild]

The Attempt at a Solution

So I have found an answer, I am just unsure if I am correct though. This is what I did:

a) gof(x)=g(f(x))
= ln(4(f(x)+1)
=ln(4e^(3x+2)+1)
[STRIKE]= ln4e^(3x+2)+ln1[/STRIKE]

b)foh(x)=f(h(x))
=e^(3(h(x))+2)
=e^(3(1/(2x-1))+2)
[STRIKE]=e^(3/(2x-1))+2)[/STRIKE]


Is this the correct working out and answers?

Neither the logarithm nor the exponential are additive functions.

ehild

 

[DJ-Smiles]

what does that mean and how does it affect my final answers?

 

[ehild]

ln(A+B)≠lnA+lnB. e^A+B≠e^A+B.
Also check your parentheses.


ehild