Let f(x)= x − 5√ x - 5 find f -1

question 7 options: f -1 (x) = x2 + 5; y ≥ 5
f -1 (x) = (x + 5)2; y ≥ 5
f -1 (x) = x2 + 25; y > 5
f -1(x) = x2 + 25; y ≥ 25

  none of the above

  (the first choice will probably be marked correct, though it is not)

You can find the inverse function by solving for y:

  x = f(y)

  x = √(y -5)

  x² = y -5

  x² + 5 = y

Then ...

  f^-1(x) = x² + 5 . . . . . matches the equation in the first selection

We note that the original function f(x) is a function by virtue of the fact that only the positive square root is of interest. That is, the range of the function f(x) is y ≥ 0. Then the inverse function will have the domain x ≥ 0.

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The offered choices seem to put restrictions on the range (y-values) of the inverse function. There is no need. The range is automatically restricted by the values the inverse function can generate (y ≥ 5). What is needed is a restriction on the domain, which must be x ≥ 0.

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Comment on the graph

The inverse of a function is the mirror image of that function reflected across the line y=x. That line is shown in dashed orange. The original function f(x) is shown in red.

The offered choice #1 for the inverse function f^-1(x) is shown in blue. As you can see, for negative values of x, there is no corresponding branch of the square root function f(x). In order to properly define the inverse function, we must make it look like the portion of the blue curve that is overlaid with purple dots. That is, we must restrict the domain of the inverse function to x ≥ 0. (The values of the inverse function will always satisfy y ≥ 5, whether we have properly restricted its domain or not.)

answer: my brother can figure it out, imma go get him so i can answer : ) edit: my brother is sleeping, sorry man

step-by-step explanation: