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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 [tex]\( f(x) = x + 3 \)[/tex], follow these detailed steps:

1. Express the function in terms of [tex]\( y \)[/tex]:
[tex]\[ y = f(x) = x + 3 \][/tex]

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

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

4. Express the inverse function [tex]\( f^{-1}(x) \)[/tex] using the solved equation:
[tex]\[ f^{-1}(x) = x - 3 \][/tex]

Therefore, the inverse function is [tex]\( f^{-1}(x) = x - 3 \)[/tex].

From the given options, the correct answer is:
[tex]\[ h(x) = x - 3 \][/tex]
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