QUESTION 5 ·1 POINT The function f(x) = 3√(x

QUESTION 5 \cdot 1 POINT The function $f(x) = 3\sqrt{x - 2} + 11$ $x \ge 2$ has an inverse $f^{-1}(x)$ defined on the domain $x \ge 11$. Find the inverse. Provide your answer below: $f^{-1}(x) = $

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00:01 So i want to find the inverse function of the given one here.

00:04 So as do that, i'm going to start with swapping out f of x for y.

00:08 And then i swap the x and y position.

00:11 So x is equal to three of the y divided by four plus three to the y.

00:17 From there, i'm going to treat that as x over one.

00:20 And i can cross multiply to turn into, if you're rid of the fractions.

00:23 So i'm going to have 4x plus x times three to the y is equal to 3 .3.

00:31 Of the y.

00:32 Okay.

00:34 From there, we'll bring three to the y over.

00:36 Well, i want to put all my three ys over, so i'll subtract this over, x times three to the y.

00:51 Okay.

00:52 So that's going to be four x is equal to three to the y minus x times three to the y.

00:58 From here, i'm going to factor out three of the y.

01:01 So i have four x is equal to three to the y multiply by one minus x.

01:09 Okay.

01:10 So from there, i'm going to divide by 1 minus x here.

01:14 And i'm going to run out of space.

01:15 I want to go ahead and rewrite it over here.

01:17 So that 4x over 1 minus x is equal to 3 to the y power.

01:21 Now, in order to undo this, i need to take log base 3 of both sides.

01:27 So take log base 3 here...

Question

QUESTION 5 \cdot 1 POINT The function $f(x) = 3\sqrt{x - 2} + 11$ $x \ge 2$ has an inverse $f^{-1}(x)$ defined on the domain $x \ge 11$. Find the inverse. Provide your answer below: $f^{-1}(x) = $

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