First question:
#f(x)=2x ^2+5# and #g(x)=2x#
#f(x)*g(x)=2x(2x^2+5)=4x^3+10x-=text(third choice)#
Second question:
#f(x)=-3x+2# and #g(x)=2x^3#
#f(x)*g(x)=2x^3(-3x+2)=-6x^4+4x^3-=text(first choice)#
#f(2)*g(3)=2(3)^3(-3(2)+2)=2(27)(-6+2)=2(27)(-4)=-8(27)=-216==-216#
#f(0)*g(3)=2(3)^3(-3(0)+2)=2(27)(2)=4(27)=108!=122#
Choose the first and third options.
Third question:
#f(x)=4x^3# and #g(x)=2x#
#(f(x))/(g(x))=(4x^3)/(2x)=2x^2-=text(second option)#
Fourth question:
The inverse function is a reflection of a function over the #y=x# plane, or when #y=f(x)# the inverse is #x=f(y)#
The point #(1,1)# appears on the original graph and on the inverse would also be #(1,1)# so choose that option.option
#(2,2)# and #(1,-1)# do not appear on the function and neither would it appear on the inverse.
#(4,2)# does appear on the function but would not appear on the inverse, since the graph has a point at #(4,2)# however the inverse would by #(2,4)# which is not a given option.
