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[tex]f(x) = {x}^{2} + 5[/tex]
[tex]y = {x}^{2} + 5[/tex]
[tex] {x}^{2} + 5 = y[/tex]
Subtract sides 5
[tex] {x}^{2} + 5 - 5 = y - 5[/tex]
[tex] {x}^{2} = y - 5[/tex]
[tex]x = ± \sqrt{y - 5} [/tex]
[tex]x≠ - \sqrt{y - 5} [/tex]
Because x is a positive number but -√y-5 is a negative number thus it's unacceptable.
So ;
[tex]x = \sqrt{y - 5} [/tex]
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[tex] {f}^{ - 1}(x) = \sqrt{x - 5} [/tex]
Done...
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