Answer:
f-1(x) = √x. +5
Step-by-step explanation:
f(x) = (x-5)^2
x = (y-5)²
√x = y-5
√x +5 = y
The inverse of the given function is required.
The inverse is [tex]g(x)=5+\sqrt{x}[/tex]
The function is
[tex]f(x)=(x-5)^2[/tex] for [tex]x\geq 5[/tex]
Isolating [tex]x[/tex]
[tex]y=(x-5)^2\\\Rightarrow \pm\sqrt{y}=x-5\\\Rightarrow x=5+\sqrt{y},5-\sqrt{y}[/tex]
Now [tex]x\geq 5[/tex]
Since, [tex]x[/tex] is not imaginary [tex]y\nless 0[/tex].
Now, [tex]5-\sqrt{y}[/tex] will not be a solution as the value of [tex]x[/tex] will become less than [tex]5[/tex] for any positive [tex]y[/tex].
Hence, the inverse is [tex]g(x)=5+\sqrt{x}[/tex]
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