Hi, there please help me and thank you in advance. Also, please show the steps as well

Question

1)If f(x)= 4x-8 and g(x)=-x²+6x-8

f(x)• g(x)

2. f(x)=2x³-5x²

g(x)=2x-1

Find (f•g)(x)

Answer 1

f(x) = 4x-8

g(x) =-x^2 +6x-8

f(x)*g(x)= f(x)g(x) = (4x-8)(-x^2+6x-8)

=-4x^3+24x^2-32x +8x^2 -48x +64

= -4x^3 +32x^2 -80x +64

unless by chance you meant to write:

(fog)(x) = f(g(x)) = f(-x^2+6x-8) = 4(-x^2+6x-8)-8

= -4x^2 +24x -32 -8

= -4x^2 +24x -40

that's how you do the 2nd question too

f(x) = 2x^3-5x^2

g(x) =2x-1

(fog)(x) = f(g(x)) = f(2x-1) = 2(2x-1)^3 -5(2x-1)^2

= 2(2x-1)(2x-1)(2x-1) - 5(2x-1)(2x-1)

=2(8x^3 -3(4x^2)(-1) +3(2x)(-1)^2 -1)

-5(4x^2 -4x +1)

= 16x^3 -24x^2 +12x -2 - 20x^2 +20x -5

= 16x^3 -44x^2 +32x -7

Answer 2

Hello Ana,

The first question is a multiplication problem involving two polynomials.

1. f(x) * g(x) = (4x-8)(-x²+6x-8) = -4x³+24x²-32x+8x²-48x+64 = -4x³+32x²-80x+64.

In this problem I multiplied the 4x by each term in g(x) and the -8 to each term in g(x), then combined like terms and simplified my answer by writing the solution in descending powers.

The second question seems to me to be a composition of functions question. The correct way to write this is (f ο g)(x) or f(g(x)).

2. f(g(x)) = 2(2x-1)³- 5(2x-1)² = 2(2x-1)(2x-1)(2x-1) -5(2x-1)(2x-1) = 2(8x^3-12x^2+6x-1) - 5(4x²-4x+1) = 16x³-24x²+12x-2-20x²+20x-5 = 16x³-44x²+32x-7

This question is similar to the first question in that it involves correctly distributing each term of one binomial into the subsequent binomials and then combining like terms at the end. The difference is that you have to plug g(x) into f(x) wherever there is an "x" term. I hope this is helpful!