Question

The functions f and g are defined by f(x)=3x, g(x)=x+ 2

a) Find an expression for (fog)(x)

b) show that f-1(18)+g-1(18)=22

Answer 1

I prefer to use the other notation, so hopefully you understand this:\[\Large (f \circ g)(x) \qquad=\qquad f\left(g(x)\right)\]They mean the same thing :)

So if we have:\[\Large f(\color{royalblue}{x})=3(\color{royalblue}{x}) \qquad\qquad \qquad g(x)=x+2\]

Then we want to plug g(x) in for our blue x that is in our f function.\[\Large f\left(\color{royalblue}{g(x)}\right)=3\left(\color{royalblue}{g(x)}\right)\]Which if we plug in the function, gives us,\[\Large f\left(\color{royalblue}{g(x)}\right)=3\left(\color{royalblue}{x+2}\right)\]