a) #f^(-1)(7)# can be read directly from the supplied diagram:
#color(white)("XXX")f^(-1)(7)=2#
b)
We are told that the function is linear.
Therefore
#color(white)("XXX")f(x)=color(green)mx+color(blue)c#
for some constants #color(green)m# and color(blue)c#
We know from the diagram that:
#color(white)("XXX")f(color(magenta)0)=color(green)m * color(magenta)0+color(blue)c=3#
#color(white)("XXX")rarr color(blue)c=color(blue)3#
also
#color(white)("XXX")f(color(magenta)2)=color(green)m * color(magenta)2 +color(blue)c= 7#
#color(white)("XXX")#and since #color(blue)c=color(blue)3#
#color(white)("XXXXXX")color(magenta)2color(green)m=4# and
#color(white)("XXXXXX")color(green)m=2#
So the function is
#color(white)("XXX")f(x)=color(green)2x+color(blue)3#
If #f(x)=11#
we have
#color(white)("XXX")color(green)2x+color(blue)3=11#
#color(white)("XXX")rarr color(green)2x=8#
#color(white)("XXX")rarr x=4#