Question

Let f(x) = 2x + 2. Solve f-1(x) when x = 4.
This literally feels like 8+2.
2(4) + 2
8 + 2
10?

Answer 1

if they asked `what is f(x) when x = 4` then you'd be correct

Answer 2

Guess I'm wrong. XD

Answer 3

they want you to find the inverse first, then plug in x = 4 into the inverse

Answer 4

How do I find it again?

Answer 5

step 1) replace f(x) with y
step 2) swap x and y
step 3) solve for y

Answer 6

f(x) = 2x + 2

y = 2x + 2

x = 2y + 2

solve for y

Answer 7

So...
Let f(x) = 2x + 2. Solve f-1(x) when x = 4.

2x = 2
2(4) = 2
8 = 2
4?

Answer 8

if you solve `x = 2y + 2` for y, what do you get?

Answer 9

xD 2 + 2 = 4
I think I'm trying to make it more complicated than it really is.

Answer 10

Is that right? It's 4?

Answer 11

step 1) replace f(x) with y
step 2) swap x and y
step 3) solve for y

f(x) = 2x + 2

y = 2x + 2 ... step 1

x = 2y + 2 ... step 2

x-2 = 2y + 2-2 ... subtract 2 from both sides

x-2 = 2y

2y = x-2

2y/2 = (x-2)/2 ... divide both sides by 2

y = (x-2)/2

So the inverse function is \[\Large f^{-1}(x) = \frac{x-2}{2}\]

Answer 12

Now you plug x = 4 into \[\Large f^{-1}(x) = \frac{x-2}{2}\]