Question

How is domain of the function f(x)=cosx restricted so that its inverse function exists?

Drag a value or interval into each box to correctly complete the statements.


The domain of f(x)=cos x is restricted to________
so that the inverse of the function exists. This means that all functional values of f(x)=cos^−1 x are on the interval__________________- .

Answer 1

see below

Explanation:

The largest interval for x ≥ 0 where cos(x) passes the horizontal line test is [0, π]. Hence the domain must be restricted to that interval if the function is to have an inverse that gives values in the range [0, π].

The domain of the function is the same as the range of the inverse function. Restricting the cos(x) function domain to x ∈ [0, π] restricts the range (functional values) of the inverse function to the same interval.