If *x* = x^2+2x-3 which of the following are true I. *x* = *x+2* II. *x* = *x-3* III. *x+2* = *x-3* (A) I only (B) II only (C) III only (D) I and II (E) I, II and III
Looking at the problem at first you can substitute *x* for f(x) so that f(x)-x^2=2x-3. so *x+2* is f(x+2). Try I. you'll find x^2+2x-3 = x^2+6x+5, then solve for x, x=-2 so I. holds true, eliminating (B), and (C). Moving on to III. we know f(x+2) is x^2+6x+5 and find that f(x-3) is x^2-4x. x^2+6x+5=x^2-4x exist for a value of x. We find x =-(1/2). So III. works, and (E) is the answer that shows I and III work so II. is also true.
For what values of x is the function f(x) = (x^2+3x+5)/(x^2+3x-4) continuous.
All values of x where the denominator is equal to zero is not continuous. All other x values are continues since both expression are polynomials which are always continuos on their own. When we set the denominator equal to zero, and find the values of x where the expression holds true, then we find the values that f(x) is not continuos since #/0 does not exist.
A rectangular prism has a volume of 8x^3 + 14 x^2+x-2 and a height of 2x+1. What is the area of the base of the prism.
Since the Volume of a rectangular prism is base X length X height, and the area is simply base X height. If we divide the given height from the volume of the prism we will find the area of the base. To divide these polynomial expression we can use long division to find A = 4x^2 + 5x-2.