For each of the following, prove that f is 1 1 on E and find f(E) a) f(x) 3x 7, E R ) f(x) el x, E (0, ) ) f(x) tan x, E ( 2, 3 2) ) f(x) x2 2x 5, E ( , 6 e) f(x) 3x x x 2 , E R ) fix) x (x2 1), E 1, 1 b) Find an explicit formula for f 1 on f() ...

a f is 11 since f x 3 0 for x R If y 3x 7 then x y 73 Therefore f1x x 73 By looking at the graph we ...

For each of the following, prove that f is 1-1 on E and find f(E). a) f(x)

Question:

For each of the following, prove that f is 1-1 on E and find f(E).
a) f(x) = 3x - 7, E = R
β) f(x) = el/x, E = (0, ∞)
γ) f(x) = tan x, E = (π/2, 3π/2)
δ) f(x) = x2 + 2x - 5, E = (-∞, -6]
e) f(x) = 3x - |x| + |x - 2|, E = R
ζ) fix) = x/(x2 + 1), E = [-1, 1]
b) Find an explicit formula for f-1 on f(£).