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I need help with number 4

I need help with number 4-example-1

2 Answers

3 votes

Answer:

D

Step-by-step explanation:

let y = f(x) and rearrange making x the subject

y =
√(x-2) + 3 ( subtract 3 from both sides )

y - 3 =
√(x-2) ( square both sides )

(y - 3)² = x - 2 ( add 2 to both sides )

(y - 3)² + 2 = x

Change y back into terms of x with x =
f^(-1) (x) , then


f^(-1) (x) = (x - 3)² + 2 → D

User Bhavesh Shah
by
8.6k points
3 votes

Answer: Choice D


f^(-1)(x) = (x-3)^2+2\\\\

============================================================

Step-by-step explanation:

First we replace f(x) with y. This is because both y and f(x) are outputs of a function.

To find the inverse, we swap x and y and solve for y like so


y = √(x-2)+3\\\\x = √(y-2)+3 \ \text{ .... swap x and y; isolate y}\\\\x-3 = √(y-2)\\\\(x-3)^2 = y-2 \ \text{ ... square both sides}\\\\(x-3)^2+2 = y\\\\y = (x-3)^2+2\\\\f^(-1)(x) = (x-3)^2+2\\\\

Note: because the range of the original function is
y \ge 3, this means the domain of the inverse is
x \ge 3. The domain and range swap roles because of the swap of x and y.

As the graph shows below, the original and its inverse are symmetrical about the mirror line y = x. One curve is the mirror image of the other over this dashed line.

I need help with number 4-example-1
User TheLibrarian
by
8.3k points

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