Q 59. - Precalculus Enhanced with Graphing Utilities

Question

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

Step-by-Step Solution

Answer

The value of$(f o g)\left(x\right)=11$and$(g o f)\left(x\right)=2$

Step 1. Given information

The given function$f\left(x\right)=2x^3-3x^2+4x-1$and$g\left(x\right)=2$

The function $(f o g)\left(x\right)=f\left(g\right(x\left)\right)$

Step 2. Substitute g ( x ) = 2 in f ( g ( x ) )

$$\begin{gathered} f\left(2\right)=2{\left(2\right)}^3-3{\left(2\right)}^2+4\left(2\right)-1 \\ f\left(2\right)=2\left(8\right)-3\left(4\right)+8-1 \\ f\left(2\right)=16-12+8-1 \\ f\left(2\right)=11 \end{gathered}$$

Step 3. The function ( g   o   f ) ( x ) = g ( f ( x ) ) Substitute f ( x ) = 2 x 3 - 3 x 2 + 4 x - 1 in g ( x ) .

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