Composite function find f(g(x))

Question

Given: f(x) = 3x^2-1 and g(x) = √5x

Find: f(g(x)) = Answer

Find the domain of f(x) = Answer

Find the domain of g(x) = Answer

Find the domain of f(g(x)) = Answer

Answer 1

f(g(x)) =

f(√5x) = 3(√5x)^2 - 1 (square root * square cancels each other as it's the inverse) therefore:-

f(√5x) = 15x² - 1

Domain of f(g(x)) = (−∞,∞)

Domain of f(x) = (−∞,∞)

Domain of g(x) = √5x = 0 ... square both sides, 5x = 0, Divide both sides by 5, x = 0 . Therefore has to be greater than or equal to zero. [0,∞)