Question

If f(x)=x^2+2x-3 and g(x)=x^2-9, find (f/g)(4) and (f+g)(4)

Answer 1

Answer:

Part 1: Find (f/g)(4) = 3

Part 2: Find (f+g)(4) = 28

Step-by-step explanation:

Part 1: Find (f/g)(4):

(f/g)(4) means divide f function by g function and simplify it. Then plug in 4 into x of that simplified function.

Let's do this:

$\frac{x^2+2x-3}{x^2-9}\\=\frac{(x+3)(x-1)}{(x-3)(x+3)}\\=\frac{x-1}{x-3}$

Plugging in 4 into x gives us:

$\frac{x-1}{x-3}\\=\frac{4-1}{4-3}\\=\frac{3}{1}\\=3$

The answer is 3

Part 2: Find (f+g)(4):

(f+g)(4) means add f function and g function and simplify it. Then plug in 4 into x of that simplified function.

Let's do this:

$(x^2+2x-3)+(x^2-9)\\=2x^2+2x-12$

Plugging in 4 into x gives us:

$2x^2+2x-12\\=2(4)^2+2(4)-12\\=28$

The answer is 28