Answer to Question #209901 in Discrete Mathematics for Sach

Question

State which of the following are not a function from R to R and why.

(a)

f(x) = 1/x

(b)

f(x) = 1/(1+x)

(c)

f(x) = (x)½

(d)

f(x) = ±(x2+1)½

(e)

f(x) = sin(x)

(f)

f(x) = ex

Answer 1

Solution:

A relation is a function if for each value of $x$, there exists a unique value of $y$ or $f(x)$.

For all of the followings, we have this condition satisfied:

(a) f(x) = 1/x

(b) f(x) = 1/(1+x)

(c) f(x) = (x)½

(e) f(x) = sin(x)

(f) f(x) = e^x

But for (d) f(x) = ±(x2+1)½, we have two values of f(x), thus it is not a function.