Question

1) Let  be a function from Z to R, such that , then  is

a) an increasing function   

b) a strictly increasing function

c) a decreasing function

d) an onto function

Answer 1

Let f be a function from Z to R, such that f(x)=x/10

So, $f(x)=\dfrac{x}{10}$

Graph of f(x) in its domain:

Now, Interval in which f(x) to be determined is ($-\infty,\infty$ )

So, a= $-\infty$ and b= $\infty$

and f(a)= $-\infty$ and f(b)= $\infty$

Hence f(a)< f(b)

Now, f'(x)= $\dfrac{1}{10}>0\ \ \ \forall \ \ x\in(-\infty,\infty)$

So, it is clear that  f(a)<f(b) and f'(x)>0

Hence f(x) is Strictly Increasing function.