Respuesta :
Answer:
[tex]f^{-1}[/tex](h) = [tex]\sqrt{h - 1}[/tex] + 1.
Step-by-step explanation:
Given, f(h) = [tex]h^{2}[/tex] - 2h + 4.
h ≥ 1 .
f(h) = [tex](h-1)^{2}[/tex] + 3.
Now, to calculate the inverse of the function we have to interchange h and f(h). {Where interchanged f(h) will represent inverse of the function}
So,
h = [tex](f(h)-1)^{2}[/tex] + 3
h - 3 = [tex](f(h)-1)^{2}[/tex]
f(h) -1 = [tex]\sqrt{h - 1}[/tex]
f(h) = [tex]\sqrt{h - 1}[/tex] + 1.
f(h) ⇒ Representing inverse of f(h) as stated above.
Thus, [tex]f^{-1}[/tex](h) = [tex]\sqrt{h - 1}[/tex] + 1.
