Q59. - Precalculus Enhanced with Graphing Utilities

Question

If $f\left(x\right)=2x^3-3x^2=4x-1$and $g\left(x\right)=2$find$(f\circ g)\left(x\right)$ and$(g\circ f)\left(x\right)$.

Step-by-Step Solution

Answer

The value of$\left(fog\right)\left(x\right)=11$and$\left(gof\right)\left(x\right)=2$.

Step 1. Given information.

The given function 
 and 

Step 2. The composite function ( f ∘ g ) x = f ( g ( x ) ) . Substitute g ( x ) = 2 in f ( g ( x ) ) .

Step 3. The composite function ( g ∘ f ) x = g ( f ( x ) )

$g(2x^3-3x^2+4x-1)=2$

Thus,$(g\circ f)\left(x\right)=2$