Question

how would you work this out?
composite function f â—¦ g

f(x) = 2e^x
g(x) = ln(x − 2)

i worked it out : 2e^(ln(x-2)
can u simplify this more?

Answer 1

Keep this in mind.

\(\ln\left(e^{x}\right) = x\cdot\ln(e) = x\)

This might lead you to the following conclusion...

\(e^{\ln(x)} = x\)

Answer 2

so is it 2(x-2) ?

Answer 3

Pretty good, but you will have to think about the Domain. It may have changed inadvertently along the way.

Answer 4

so domain will be x cannot equal 2

Answer 5

The Domain of g(x) is \(x-2 \ge 0 \implies x \ge 2\)

f(x) has no restriction.