Questions: If f(g)=2g+2 and g(x)=-2x, what is f(g(x)) in terms of x?

Transcript text: If $f(g)=2 g+2$ and $g(x)=-2 x$, what is $f(g(x))$ in terms of $x$ ?

Solution

Solution Steps

To find $ f(g(x)) $, we need to substitute $ g(x) $ into the function $ f(g) $. First, we find $ g(x) = -2x $. Then, substitute $ g(x) $ into $ f(g) = 2g + 2 $ to get $ f(g(x)) = 2(-2x) + 2 $.

Step 1: Define the Functions

We are given two functions: $ f(g) = 2g + 2 $ and $ g(x) = -2x $. Our goal is to find $ f(g(x)) $.

Step 2: Substitute $ g(x) $ into $ f(g) $

Substitute $ g(x) = -2x $ into the function $ f(g) $. This gives us: \[ f(g(x)) = 2(-2x) + 2 \]

Step 3: Simplify the Expression

Simplify the expression obtained in the previous step: \[ f(g(x)) = -4x + 2 \]

Final Answer

The expression for $ f(g(x)) $ in terms of $ x $ is: \[ \boxed{-4x + 2} \]

Was this solution helpful?

Unhelpful

Helpful

Questions asked by other users

< Previous Next >