Question

The function f is defined by

f(x) ≡ 2 + ln (3x − 2), x ∈ , x > 2
3 .

(a) Find the exact value of ff(1). (2)

(b) Find an expression for f −1
(x).

Answer 1

part a) f(1)= 2+ln1
so ff(1)= 2+ln(3(2+ln1)-2) = 2+ln 4

Answer 2

I don't think so because f(x) is defined 2 + ln (3x − 2) for x>2, so f(1) could be different.

Not really sure, though

Answer 3

what about part b? I think im right for part a I just cant do part b :/

Answer 4

oh wait.... y=2+ln(3x-2)
so y-2=ln(3x-2)
e^(y-2)=3x-2
1/3(e^(y-2)+2)=x
so inverse function = 1/3(e^(x-2)+2)