Question

let ( f(x) = 2x - 1 ) and ( g(x) = 3x ). identify the rules for the following functions
a. ( f(g(2)) )
b. ( f(g(x)) )

Explanation:

Part a: \( f(g(2)) \)

Step 1: Find \( g(2) \)

We know that \( g(x) = 3x \). To find \( g(2) \), we substitute \( x = 2 \) into \( g(x) \).
\( g(2)=3\times2 = 6 \)

Step 2: Find \( f(g(2)) \)

Now we need to find \( f(6) \) because \( g(2) = 6 \). We know that \( f(x)=2x - 1 \). Substitute \( x = 6 \) into \( f(x) \).
\( f(6)=2\times6 - 1=12 - 1 = 11 \)

Step 1: Substitute \( g(x) \) into \( f(x) \)

We know that \( f(x)=2x - 1 \) and \( g(x)=3x \). We substitute \( g(x) \) (which is \( 3x \)) in place of \( x \) in the function \( f(x) \).
So \( f(g(x))=f(3x) \)

Step 2: Simplify \( f(3x) \)

Now we use the rule of \( f(x) \) which is \( 2x - 1 \). Substitute \( x = 3x \) into \( f(x) \).
\( f(3x)=2\times(3x)-1 = 6x - 1 \)

Answer:

\( 11 \)

Part b: \( f(g(x)) \)