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

simplifying

5(x + -6) = 2(x + 3)

reorder the terms:

5(-6 + x) = 2(x + 3)

(-6 * 5 + x * 5) = 2(x + 3)

(-30 + 5x) = 2(x + 3)

reorder the terms:

-30 + 5x = 2(3 + x)

-30 + 5x = (3 * 2 + x * 2)

-30 + 5x = (6 + 2x)

solving

-30 + 5x = 6 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-30 + 5x + -2x = 6 + 2x + -2x

combine like terms: 5x + -2x = 3x

-30 + 3x = 6 + 2x + -2x

combine like terms: 2x + -2x = 0

-30 + 3x = 6 + 0

-30 + 3x = 6

add '30' to each side of the equation.

-30 + 30 + 3x = 6 + 30

combine like terms: -30 + 30 = 0

0 + 3x = 6 + 30

3x = 6 + 30

combine like terms: 6 + 30 = 36

3x = 36

divide each side by '3'.

x = 12

simplifying

x = 12

this should .