What is g(f(x)) when f(x) = 5x + 3, and g(x) = 3x2 + 3?

g(f(x)) =75x² + 90x + 30

Step-by-step explanation:

To find g(fx), all we need to do is to insert f(x) in g(x), that is anywhere x is in g(x), we replace the value of g(x) with x and then simplify

f(x) = 5x + 3         g(x) = 3x² + 3

g(f(x))  =  3(5x + 3)²  +  3

Next is to open the parenthesis and then simplify

(5x + 3)² = (5x + 3)(5x + 3)  = 5x(5x+3) + 3(5x+3) =25x² +15x +15x+9 = 25x²+30x+9

g(f(x)) = 3(25x² + 30x + 9) +  3

g(f(x)) = 75x² + 90x + 27 + 3

g(f(x)) =75x² + 90x + 30

d

step-by-step explanation:

see explanation

step-by-step explanation:

since the sequence is geometric there is a common ratio r between consecutive terms, that is

r = 4 ÷ - 2 = - 2

r = - 8 ÷ 4 = - 2

r = 16 ÷ 8 = - 2

the next term - 13 must be incorrect as it should be - 32 for the sequence to be geometric.

the first 4 terms are therefore geometric with common ratio r = - 2