Answer :
To find the inverse of the function \( f(x) = 4x \), we will follow these steps:
1. Express the function in terms of \( y \) instead of \( f(x) \):
[tex]\[ y = 4x \][/tex]
2. Swap \( x \) and \( y \) to find the inverse:
[tex]\[ x = 4y \][/tex]
3. Solve for \( y \) to express the inverse function in terms of \( x \):
[tex]\[ y = \frac{x}{4} \][/tex]
Thus, the inverse function can be written as:
[tex]\[ h(x) = \frac{x}{4} \][/tex]
4. Among the given choices, the one that matches our derived inverse function is:
[tex]\[ h(x) = \frac{1}{4}x \][/tex]
Therefore, the correct answer is:
[tex]\[ \boxed{4} \][/tex]
1. Express the function in terms of \( y \) instead of \( f(x) \):
[tex]\[ y = 4x \][/tex]
2. Swap \( x \) and \( y \) to find the inverse:
[tex]\[ x = 4y \][/tex]
3. Solve for \( y \) to express the inverse function in terms of \( x \):
[tex]\[ y = \frac{x}{4} \][/tex]
Thus, the inverse function can be written as:
[tex]\[ h(x) = \frac{x}{4} \][/tex]
4. Among the given choices, the one that matches our derived inverse function is:
[tex]\[ h(x) = \frac{1}{4}x \][/tex]
Therefore, the correct answer is:
[tex]\[ \boxed{4} \][/tex]
