Question

Algebra 2 - Composition Functions

#4-6: let f(x)= 5x^3-2x and g(x)= 3x^3. Perform the indicated operation.

Answer 1

`f(x) = 5x {}^(3) - 2x \\ g(x) = 3x {}^(3)`

4)

`(f(x))/(g(x)) = \frac{5x {}^(3) - 2x }{3x {}^(3) } = \frac{x(5x {}^(2) - 2)}{3x {}^(3) } = \frac{5x {}^(2) - 2}{3x^2}`

5)

`f(g(x)) = 5( 3x {}^(3) ) {}^(3 ) - 2(3x {}^(3) ) \\ f(g(x)) = 135x {}^(9) - 6x {}^(3)`

6)

`g(f(x)) = 3(5x {}^(3) - 2x) {}^(3) \\ g(f(x)) = 3(125x {}^(9) - 150x {}^(7) + 60x {}^(5) - 8x {}^(3) ) \\ g(f(x) )= 375x {}^(9) - 450x {}^(7) + 180x {}^(5) - 24x {}^(3)`