Question

For the function f(x)=rac{\sqrt{x} }{5} +2" alt="\frac{\sqrt{x} }{5} +2" align="absmiddle" class="latex-formula">
A. ƒ –1(x) = 25(x – 2)2, x ≥ 2

B. ƒ –1(x) = 25x2 – 2, x ≥ 0

C. ƒ –1(x) = 5(x – 2)2, x ≥ 0

D. ƒ –1(x) = 25(x – 2)2, x ≥ 0

Answer 1

Answer:

$f^{-1}(x)=25(x-2)^2$

Step-by-step explanation:

The inverse function can be found by solving ...

  f(y) = x

  (√y)/5 +2 = x

  (√y)/5 = x -2 . . . . . subtract 2

  √y = 5(x -2) . . . . . . multiply by 5

  y = 25(x -2)² . . . . . square both sides

The inverse function is ...

  $f^{-1}(x)=25(x-2)^2$

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About the graph

The inverse of a function is its mirror image across the line y = x.