(E) Interchange x and y: x = y 3 + 2
Solve for y: y 3 = x − 2, so .
(D) Since f(1) = 0, x − 1 is a factor of f. Since f(x) divided by x − 1 yields
x^2 − x − 2, f(x) = (x − 1) (x + 1) (x − 2); the roots are x = 1, −1, and 2.
(B) If , then −∞ < tan x < ∞ and 0 < etan x < ∞.
(A) The reflection of f(x) in the x-axis is −f(x).
(C) f(x) attains its maximum when sin does. The maximum value of
the sine function is 1; the smallest positive occurrence is at . Set equal
to .
(A).
(A) Interchange x and y: x = 2e−y
Solve for .
Thus .
(C) The function in (C) is not one-to-one since, for each y between
