Question

1. $g(n) = -3n - 3$

$h(n) = 3n^2 - n$
find $(g + h)(7)$

1. $g(x) = x^2 + 3$

$h(x) = x + 4$
find $(g - h)(10)$

Explanation:

(Problem 6):

Step1: Define $(g+h)(n)$

$(g+h)(n) = g(n) + h(n) = (-3n-3) + (3n^2 - n)$

Step2: Simplify the expression

$(g+h)(n) = 3n^2 -4n -3$

Step3: Substitute $n=7$

$(g+h)(7) = 3(7)^2 -4(7) -3$

Step4: Calculate each term

$3(7)^2=3\times49=147$, $4(7)=28$

Step5: Compute final value

$(g+h)(7)=147-28-3=116$

(Problem 8):

Step1: Define $(g-h)(x)$

$(g-h)(x) = g(x) - h(x) = (x^2+3) - (x+4)$

Step2: Simplify the expression

$(g-h)(x) = x^2 -x -1$

Step3: Substitute $x=10$

$(g-h)(10) = (10)^2 -10 -1$

Step4: Calculate each term

$(10)^2=100$

Step5: Compute final value

$(g-h)(10)=100-10-1=89$

Answer:

1. $(g+h)(7) = 116$
2. $(g-h)(10) = 89$