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Complete the steps in order to write the inverse of [tex][tex]$f(x)=x+5$[/tex][/tex].

1. [tex]y = x + 5[/tex]
2. [tex]x = y + 5[/tex]
3. [tex]x - 5 = y[/tex]
4. [tex]f^{-1}(x) = x - 5[/tex]

Sagot :

GinnyAnsweridn
To find the inverse of the function [tex]\( f(x) = x + 5 \)[/tex], we follow a series of steps:

1. Replace [tex]\( f(x) \)[/tex] with [tex]\( y \)[/tex]:
[tex]\[ y = x + 5 \][/tex]

2. Swap [tex]\( x \)[/tex] and [tex]\( y \)[/tex] to find the inverse function equation:
[tex]\[ x = y + 5 \][/tex]

3. Solve the equation for [tex]\( y \)[/tex]:
[tex]\[ x - 5 = y \][/tex]

4. Replace [tex]\( y \)[/tex] with [tex]\( f^{-1}(x) \)[/tex]:
[tex]\[ y = x - 5 \][/tex]

So, filling in the blanks in the steps provided:

1. [tex]\( y \)[/tex] [tex]\( = x + 5 \)[/tex]
2. [tex]\( x \)[/tex] [tex]\( = y + 5 \)[/tex]
3. [tex]\( x - 5 \)[/tex] [tex]\( = y \)[/tex]
4. [tex]\( y \)[/tex] [tex]\( = x - 5 \)[/tex]

Thus, the inverse function [tex]\( f^{-1}(x) \)[/tex] is:

[tex]\[ f^{-1}(x) = x - 5 \][/tex]
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