Question

Let f and g be functions from $\left\{1,2,3,4\right\}$to $\left\{a,b,c,d\right\}$and from $\left\{a,b,c,d\right\}$to $\left\{1,2,3,4\right\}$, respectively, with $f\left(1\right)=d$, $f\left(2\right)=c$, $f\left(3\right)=a$and $f\left(4\right)=b$, and $g\left(a\right)=2$, $g\left(b\right)=1$, $g\left(c\right)=3$,and $g\left(d\right)=2$

a) Is f one-to-one? Is g one-to-one?

b) Is f onto? Is g onto?

c) Does either f or g have an inverse? If so, find this inverse.

Short answer

a) Yes, no

b) Yes, no

c) f has inverse with $f^{-1}\left(a\right)=3,f^{-1}\left(b\right)=4,f^{-1}\left(c\right)=2,f^{-1}\left(d\right)=1;g$has no

Step-by-step solution

Step: 1

d) Yes, no

e) Yes, no

f) f has inverse with $f^{-1}\left(a\right)=3,f^{-1}\left(b\right)=4,f^{-1}\left(c\right)=2,f^{-1}\left(d\right)=1;g$has no inverse