Question

To which interval would we restrict f(x) = cos (x-π/4) so that f(x) is invertible?

Answer 1

Answer:

The range of x values for which y is unique is 2·π

Step-by-step explanation:

For a function j: X → Y to be invertible, we have that for every y in Y, there is associated only one x which is an element of x

Hence, f(x) = cos(x - π/4) gives

the x intercept at two penultimate points of the graph of cos(x - π/4) are;

x = 2.36, and x = 8.64

x = 3/4·π, and x = 2.75·π = $2\tfrac{3}{4}\cdot \pi$

Hence the range of x values for which y is unique is presented as follows

$2\tfrac{3}{4}\cdot \pi - \frac{3}{4}\cdot \pi = 2}\cdot \pi$

The range of x values for which y is unique = 2·π.