For the pair of functions, find the indicated sum, difference, product, or quotient. f(x) = 16 - x2; g(x) = 4 - x find (f + g)(x). a) -x2 + x + 12 b) x3 - 4x2 - 16x + 64 c) 4 + x d) -x2 - x + 20

Hello!

if you have two functions f(x) and g(x) the sum of them f(x) + g(x) is represented as (f + g)(x)

then if our functions are f(x) = 16 - x^2 and g(x) = 4 - x

then (f + g)(x) = f(x) + g(x) = (16 - x^2) + (4 - x) = 20 - x^2 - x

then the correct answer is d.

if we want to find the difference (f -g)(x), we just do the direct difference.

(f - g)(x) = f(x) - g(x) =  (16 - x^2) - (4 - x) = 12 + x -x^2

where the correct answer is the a.

the product (f*g)(x) is the direct product.

(f*g)(x) = f(x)*g(x) = (16 - x^2)*(4 - x) = 16*4 - 16x - 4x^2 + x^3 = x^3 - 4x^2 - 16x + 64

then the correct answer is b.

For the quotient we have (f/g)(x) wich is the direct quotient between f(x) and g(x)

now is usefull to know that (a^2 - b^2) = (a + b)(a - b)

then f(x) = 16 - x^2 = 4^2 - x^2 = (4 + x)(4 - x)

then:

(f/g)(x) = f(x)/g(x) = ( (x+4)(4-x)/(4-x)) = x + 4

then the correct answer is c.