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What is the inverse of the function [tex]f(x) = x + 3[/tex]?

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

Sagot :

GinnyAnswer
To find the inverse of the function \( f(x) = x + 3 \), we need to follow these steps:

1. Set the function equal to \( y \):
[tex]\[ y = x + 3 \][/tex]

2. Swap \( x \) and \( y \):
[tex]\[ x = y + 3 \][/tex]

3. Solve for \( y \) to express \( y \) in terms of \( x \):
[tex]\[ y = x - 3 \][/tex]

So, we have determined that the inverse function is \( h(x) = x - 3 \).

Upon comparing this with the provided options:
- \( h(x) = \frac{1}{3}x + 3 \)
- \( h(x) = \frac{1}{3}x - 3 \)
- \( h(x) = x - 3 \)
- \( h(x) = x + 3 \)

The correct inverse function is \( h(x) = x - 3 \). Therefore, the correct option is:

[tex]\( h(x) = x - 3 \)[/tex].
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