See answer
f(x) = (x+1)2 , g(x) = 2(x-1)
a. Show that gf(x) = 2x(x+2)Recognize that you put f(x) "into" g(x)Replace x in g(x) with f(x)2[(x+1)2-1]2[x2+2x+1-1]2(x2+2x)2x2+4x, now factorise this2x(x+2)
b. find g-1(7)First find g-1(x)Replace g with yy = 2(x-1)Swap y and x to find inverse, then rearrange for yx = 2(y-1)x= 2y - 2x + 2 = 2yy = x+2/2therefore g-1(x) = x+2/2
Now sub x=7 into g-1(x)7+2/29/2= 4.5
