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How to work out range from functions C3?

Can someone please explain how you work this out? ( I know the final answer because of the mark scheme but it doesnt say the method therefore i don't know how to do it for other examples)
ALSO: one thing i do know is that range of f -1 (x) = domain f(x) and vice versa


9. The function f has domain [1, ) and is defined by
f (x) = ln (3x 2) + 5 .
(a) Find an expression for f –1(x). [4]
(b) State the domain of f –1. [1]



10. The functions f and g have domains [ 3,infinity ) and (– infinity,infinity ) respectively and are defined by
f (x) = ,square root of (x + 4)
g (x) = 2x2 3.
(a) Write down the range of f and the range of g. [2]
(b) Find an expression for gf (x). Simplify your answer. [2]
(c) Solve the equation fg(x) = 17. [4]
Reply 1
For f(x) = ln(3x-2) + 5, the range is the set of values of f(x). When x = 1, we have ln(1) + 5 = 0 + 5 = 5. f(x) then increases to infinity as x goes to infinity.

As you said, you know that the domain of f^-1(x) is the range of f(x).

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