To find the inverse of the function [tex]\( f(x) = 4x \)[/tex], we need to follow a series of steps:
1. Express the function as an equation in terms of [tex]\( y \)[/tex]:
[tex]\[ y = 4x \][/tex]
2. Solve for [tex]\( x \)[/tex] in terms of [tex]\( y \)[/tex]:
To isolate [tex]\( x \)[/tex], we divide both sides of the equation by 4:
[tex]\[ x = \frac{y}{4} \][/tex]
3. Replace [tex]\( y \)[/tex] with [tex]\( x \)[/tex] to write the inverse function:
The inverse function [tex]\( h(x) \)[/tex] is given by:
[tex]\[ h(x) = \frac{x}{4} \][/tex]
Thus, the inverse function of [tex]\( f(x) = 4x \)[/tex] is [tex]\( h(x) = \frac{1}{4} x \)[/tex].
Now, let's check the given options to find which one correctly represents the inverse function:
- [tex]\( h(x) = x + 4 \)[/tex] → Incorrect
- [tex]\( h(x) = x - 4 \)[/tex] → Incorrect
- [tex]\( h(x) = \frac{3}{4} x \)[/tex] → Incorrect
- [tex]\( h(x) = \frac{1}{4} x \)[/tex] → Correct
Therefore, the correct option is:
[tex]\[ h(x) = \frac{1}{4} x \][/tex]
