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Which represents the inverse of the function [tex]f(x) = 4x[/tex]?

A. [tex]h(x) = x + 4[/tex]
B. [tex]h(x) = x - 4[/tex]
C. [tex]h(x) = \frac{3}{4}x[/tex]
D. [tex]h(x) = \frac{1}{4}x[/tex]


Sagot :

To find the inverse of the function [tex]\( f(x) = 4x \)[/tex], we need to find a function [tex]\( h(x) \)[/tex] such that when we apply [tex]\( h \)[/tex] to [tex]\( f(x) \)[/tex], we get back to [tex]\( x \)[/tex]. Here's the step-by-step process to find the inverse:

1. Start with the function:
[tex]\[ f(x) = 4x \][/tex]

2. Replace [tex]\( f(x) \)[/tex] with [tex]\( y \)[/tex]:
[tex]\[ y = 4x \][/tex]

3. Solve for [tex]\( x \)[/tex] in terms of [tex]\( y \)[/tex]:
[tex]\[ y = 4x \implies x = \frac{y}{4} \][/tex]

4. Replace [tex]\( y \)[/tex] with [tex]\( x \)[/tex] to express the inverse function:
[tex]\[ h(x) = \frac{x}{4} = \frac{1}{4}x \][/tex]

Thus, the inverse function of [tex]\( f(x) = 4x \)[/tex] is:
[tex]\[ h(x) = \frac{1}{4} x \][/tex]

Among the given options, the correct representation of the inverse function is:
\[
h(x) = \frac{1}{4} x
\
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