Question

math 30 pre - calculus
chapter 10
review
name: ella
answer all questions in the space provided. you must show a full solution in order marks. good luck!

1. given ( f(x)=2x - 1 ) and ( g(x)=x^{2}+4 ), determine each of the following:

a.) ( (f + g)(-3) ) b.) ( (g - f)(4) )
c.) ( f(0)cdot g(1) ) d.) ( \frac{f(0)}{g(-2)} )
e.) ( f(g(x)) ) f.) ( g(f(x)) )

Explanation:

Part a: \((f + g)(-3)\)

Step1: Define \((f + g)(x)\)

\((f + g)(x)=f(x)+g(x)=(2x - 1)+(x^{2}+4)=x^{2}+2x + 3\)

Step2: Substitute \(x=-3\)

\((f + g)(-3)=(-3)^{2}+2\times(-3)+3=9-6 + 3\)

Step3: Calculate the result

\(9-6 + 3=6\)

Step1: Define \((g - f)(x)\)

\((g - f)(x)=g(x)-f(x)=(x^{2}+4)-(2x - 1)=x^{2}-2x+5\)

Step2: Substitute \(x = 4\)

\((g - f)(4)=4^{2}-2\times4 + 5=16-8 + 5\)

Step3: Calculate the result

\(16-8 + 5=13\)

Step1: Find \(f(0)\)

\(f(0)=2\times0-1=-1\)

Step2: Find \(g(1)\)

\(g(1)=1^{2}+4=5\)

Step3: Multiply the results

\(f(0)\cdot g(1)=(-1)\times5=-5\)

Answer:

\(6\)

Part b: \((g - f)(4)\)