Question

A function f(x) = -1 for all values of x. Another function g(x) = 3x for all values of x. What is g(f(x)) when x = 4?

• A. -12
• B. -3
• C. 3
• D. -1
• E. 12

Hint:

When a constant function is the inner function in a composition, like \(g(f(x))\) where \(f(x) = c\), the final result will be \(g(c)\) and will not depend on the initial variable \(x\). The specific value of \(x\) (in this case, \(x=4\)) is irrelevant to the final answer.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
This problem involves the composition of two functions, \(g(f(x))\), where one of the functions, \(f(x)\), is a constant function. A constant function always outputs the same value, regardless of the input.
Step 2: Detailed Explanation:
We are asked to find the value of \(g(f(x))\) when \(x = 4\), which can be written as \(g(f(4))\).
First, we must evaluate the inner function, \(f(4)\).
The problem states that \(f(x) = -1\) for all values of \(x\). This means that no matter what input we provide for \(f\), the output will always be -1.
Therefore, \(f(4) = -1\).
Now we can substitute this result into the outer function, \(g(x)\).
We need to find \(g(f(4))\), which is now \(g(-1)\).
The function \(g(x)\) is given by \(g(x) = 3x\).
Substitute \(x = -1\) into \(g(x)\):
\[ g(-1) = 3(-1) \] \[ g(-1) = -3 \] Step 3: Final Answer:
The value of \(g(f(x))\) when \(x = 4\) is -3.