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If [tex]\( f(x) = 5x \)[/tex], what is [tex]\( f^{-1}(x) \)[/tex]?

A. [tex]\( f^{-1}(x) = -5x \)[/tex]
B. [tex]\( f^{-1}(x) = -\frac{1}{5}x \)[/tex]
C. [tex]\( f^{-1}(x) = \frac{1}{5}x \)[/tex]
D. [tex]\( f^{-1}(x) = 5x \)[/tex]

Sagot :

GinnyAnswer
To find the inverse function [tex]\( f^{-1}(x) \)[/tex] of the function [tex]\( f(x) = 5x \)[/tex], we can use the following steps:

1. Express the function in terms of [tex]\( y \)[/tex]:
Let [tex]\( y = f(x) \)[/tex]. Therefore, we have:
[tex]\[ y = 5x \][/tex]

2. Swap [tex]\( x \)[/tex] and [tex]\( y \)[/tex]:
To find the inverse function, we interchange the roles of [tex]\( x \)[/tex] and [tex]\( y \)[/tex]:
[tex]\[ x = 5y \][/tex]

3. Solve for [tex]\( y \)[/tex]:
Isolate [tex]\( y \)[/tex] by dividing both sides of the equation by 5:
[tex]\[ y = \frac{x}{5} \][/tex]

4. Conclusion:
The inverse function [tex]\( f^{-1}(x) \)[/tex] is:
[tex]\[ f^{-1}(x) = \frac{x}{5} \][/tex]

To write it in a simplified form, we can also express it as:
[tex]\[ f^{-1}(x) = \frac{1}{5}x \][/tex]

Therefore, the correct choice from the given options is:
[tex]\[ f^{-1}(x) = \frac{1}{5} x \][/tex]
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