State whether f(x) = tanx – x is increasing or decreasing its domain.

If g(x) is a decreasing function on R and f(x) = tan^–1 {g(x)}. State whether f(x) is increasing or decreasing on R.

Write the set of values of a for which the function f(x) = ax + b is decreasing for all xϵR.

Write the interval in which f(x) = sin x + cos x, xϵ[0, π/2] is increasing.

Write the set of values of a for which f(x) = cosx + a²x + b is strictly increasing on R.