Functions?

Question

State the image set of the following functions:
(a) f: [-2,3] maps to R
f: x maps to x^2

(b) G: ]0,pi/4[ maps to R note pi = 3.141592654
g: x maps to Cosx

Answer 1

Given a subset of the domain, such as [-2, 3] which is a subset of all real numbers, the "image set" of the subset is the corresponding subset of the domain.

a) The set [-2, 3] is a closed interval.
f(x) = x²

(-2)² = 4 and 3² = 9, but 0 is also in the interval, and 0² = 0.

So the image set is [0, 9]. In other words for any real number between 0 and 9, you can find an x-value between -2 and 3 that gives you that number when squared.

b) I'm not familiar with the notation ] [, I'm going to assume you mean [0, pi/4].

g(x) = cos x

cos(0) = 1, cos (pi/4) = 0, and there is no value in [0,pi/4] that gives you a cosine of less than 0 or greater than 1.

So the image set is [0,1].