Question 1128079


f(x)={(1,4),(2,2),(8,3),(3,3),(-7,1),(8,-1)}

The relation is not a function.
Since {{{x=8 }}}produces {{{y=3 }}}and{{{ y=-1}}}, the relation  is {{{not}}} a function.


a) Determine the value of {{{f(3)}}}

from given points you see that  {{{f(3)=3}}}

b) Solve {{{f(x) = 2}}}
from given points you see that {{{f(2) = 2}}}->{{{x=2}}}

c) Determine {{{f^-1(4)}}} 

The inverse of a function differs from the function in that all the x-coordinates and y-coordinates have been switched. That is, if ({{{4}}},{{{6}}}) is a point on the graph of the function, then ({{{6}}},{{{4}}}) is a point on the graph of the inverse function.

so, since we have no point where {{{x=4}}} there is no inverse  {{{f^-1(4)}}} 

d) Determine if{{{ f^-1}}} is a function. 

if  f(x)={(1,4),(2,2),(8,3),(3,3),(-7,1),(8,-1)}, inverse will be

f^-1 (x)={(4,1),(2,2),(3,8),(3,3),(1,-7),(-1,8)}

since {{{x=3 }}}produces {{{y=8}}} and {{{y=3}}}, the relation is {{{not}}} a function

e) What is the domain and range? 

the domain and range of given relation:

domain={-7,-1,1,2,3,8}
range={-1,1,2,3,4}

the domain and range of inverse:
domain={-1,1,2,3,4}
range={-7,-1,1,2,3,8}