The defining equations for the function f is f(x) = 3x^2 + 1. The defining equation for the function g is g(x) = 2x-3. Then the defining equation for f \circle g (x) is:

Question

The defining equations for the function f is f(x) = 3x^2 + 1.  The defining equation for the function g is g(x) = 2x-3.    Then the defining equation for  f \circle g (x) is:

anonymous · Answer

10x^2-5x-5
       12x^2-36x+28
       6x^2 + 28
       5x^3 - 12x^2 + 9x - 1

anonymous · Answer

@phi @binks

anonymous · Answer

@jim_thompson5910

jim_thompson5910 · Answer

$$\Large f \circ g$$ is the same as f(g(x))

jim_thompson5910 · Answer

ie $$\Large (f \circ g)(x) = f(g(x))$$

jim_thompson5910 · Answer

$$\Large f(x) = 3x^2 + 1$$


$$\Large f(g(x)) = 3(g(x))^2 + 1$$


$$\Large f(g(x)) = 3(2x-3)^2 + 1$$


$$\Large f(g(x)) = 3(2x-3)(2x-3) + 1$$


$$\Large f(g(x)) = 3(4x^2-12x+9) + 1$$


$$\Large f(g(x)) = 12x^2-36x+27 + 1$$


$$\Large f(g(x)) = 12x^2-36x+28$$


$$\Large (f \circ g)(x) = 12x^2-36x+28$$