If f(x)= [x], where [x] donates the greatest integer less than or equal to x, and g(x)=-1/x, then f(g(3))=?

Question

the choices are:

a)-3

b)-1

c)0

d)1

e)3

Answer 1

g(x) = -1/x

g(3) = -1/3

 

f(g(3)) = f(-1/3) = [-1/3] = -1

 

If you plot -1/3 on a number line (below). the solution for ≤ -1/3 lies from -1/3 to the left.  The first integer you bump into is -1.  As you go further left, the numbers get more negative and hence smaller.  So the largest integer ≤ -1/3 is -1.

                                  -1/3

<-----|------|------|-----]--|--------|--------|-------->

        -3         -2      -1      0         1          2

Answer 2

f(g(3)) = f(-1/3) = [-1/3] = greatest integer less than or equal to -1/3

 

                                      = -1