**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**

The **Answer to the Question**

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**Here's the Solution to this Question**

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) = ex

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