Let f(x) = 3x + 2 and g(x) = 7x + 6 . find f g and it’s domain

Solution for f • g:

The notation f • g or f(g(x)) means that we need to plug the equation from g(x) into every x variables in the function f(x). We do this by following the steps below and by simplifying accordingly:

ANSWER: f(g(5)) is equal to 21x + 20.

Domain:

For the function f(g(x)), we can find the domain by analyzing the domains of each individual functions separately and excluding certain values depending on the restrictions from the outermost function.

However, since both functions have all real numbers as its domain, we will not need to do any exclusion anymore.

ANSWER: The domain of the function is all real numbers.

answer is 8x+24

area of vanessa's patio = length × width

given, length = (3x² + 5x + 10)

width = (x² - 3x - 1)

area of vanessa's patio = (3x² + 5x + 10)(x² - 3x - 1)

= 3x²(x² - 3x - 1) + 5x(x² - 3x - 1) + 10(x² - 3x - 1)

= 3x⁴ - 9x³ - 3x² + 5x³ - 15x² - 5x + 10x² - 30x - 10

= 3x⁴ - 4x³ - 8x² - 35x - 10

hence, expression of vanessa's patio = (3x⁴ - 4x³ - 8x² - 35x - 10)