Answer:2a) [tex]g(x)=3x-6[/tex]2b) This is a show kind of answer. The showing of this in the explanation.2c) I provided the graph. The lines should be a reflection through the y=x line. The points (a,b) on y=(1/3)x+2 or swapped to get the points (b,a) on y=3x-6. That is for, example the point (-3,1) is on y=(1/3)x+2 while (1,-3) is on y=3x-6.Step-by-step explanation:2a) The inverse of a function is you just swapping x and y around. You also almost always asked to remake y the subject after that though.So anyways we have this equation [tex]y=\frac{1}{3}x+2[/tex] to represent that function you have there.We want to swap x and y:[tex]x=\frac{1}{3}y+2[/tex]Now we want to solve for y.Subtract 2 on both sides:[tex]x-2=\frac{1}{3}y[/tex]Multiply both sides by 3:[tex]3(x-2)=y[/tex][tex]y=3(x-2)[/tex]Distribute:[tex]y=3x-6[/tex]So they want us to name the inverse g(x).[tex]g(x)=3x-6[/tex]2b) We want to show by composition that these functions are inverses. That is we want to show f(g(x))=x and g(f(x))=x.Let's do that:f(g(x))Replace g(x) with 3x-6 since g(x)=3x-6.f(3x-6)Replace the old input x with the new input (3x-6) in (1/3)x+2.[tex]\frac{1}{3}(3x-6)+2[/tex]Distribute:[tex]\frac{3x}{3}-\frac{6}{3}+2[/tex]Simplify:[tex]x-2+2[/tex][tex]x-0[/tex][tex]x[/tex].So we do have f(g(x))=x.Now to show the other way:g(f(x))Replace f(x) with (1/3)x+2 since f(x)=(1/3)x+2.g((1/3)x+2)Replace the old input x with the new input (1/3)x+2 in 3x-6.3((1/3)x+2)-6Distribute:[tex]3(\frac{1}{3})x+3(2)-6[/tex]Simplify:[tex]1x+6-6[/tex][tex]x+6-6[/tex][tex]x+0[/tex][tex]x[/tex]So we do have g(f(x))=x.We have confirmed that f and g are indeed inverses since f(g(x))=x and g(f(x))=x.2c) Visually if two functions are inverses they should be reflections through the y=x line so that is what we should see since f and g are inverses.I going to compare both equations to y=mx+b form to determine the y-intercept and the slope.y=mx+by=(1/3)x+2 tells us the slope is 1/3 and the y-intercept is 2.y=3x-6 tells us the slope is 3 and the y-intercept is -6. I have color-coded the picture.