Question

Given the function f(x) = 4(x+3) – 5, solve for the inverse function when x = 3.

Answer 1

@johnweldon1993 this is my last question, if you don't mind!

Answer 2

Alright, so here...we need the inverse...and then plug in that value x = 3

have you done inverses before?

Answer 3

Yes but they are VERY new to me. This is my first year of Algebra 2.

Answer 4

Ah, well welcome, it only gets harder from here >.< lol no, just kidding :P

So

For inverses...all we need to do...is switch the positions of the 'x' and the 'y'...and then solve for the 'y' again

Answer 5

So here we have

\[\large y = 4(x + 3) - 5\]

Answer 6

Switch the 'x' and the 'y'

\[\large x = 4(y + 3) - 5\]

Answer 7

and use algebra to solve for 'y' again...

how would we do that?

Answer 8

Combine terms (not sure if that's the proper term) to get 4y+7?

Answer 9

Indeed :)

so we have
\[\large x = 4y + 7\]

so solving that for 'y' we get?

Answer 10

x-4y=7?

Answer 11

Not quite :)

so what the whole idea is...is to isolate the 'y'

because eventually we want

y = ...something right?

So where we have

\[\large x = 4y + 7\]

We want y by itself....so we need to move everything else to the other side of the equation

If we subtract 7 from both sides that will isolate the 4y...so that's a start!

\[\large x - 7 = 4y\]

Now...if we want to solve for y (not 4y) what do we do?

Answer 12

Hm. I'm not sure.

Answer 13

Well...

\[\large 4y = x - 7\]

Lets see...we have a 4 being MULTIPLIED to the 'y'....so to cancel that...we do what is opposite of multiplication...which is division

Since 4 is being multiplied to the y...if we divide that by 4...we will have

\[\large \frac{4y}{4} = y\]

which is what we want right? we wanted to just have 'y'

So that's what we need to do...we need to divide everything by 4

\[\large \frac{x - 7 = 4y}{4}\]

\[\large \frac{x - 7}{4} = y\]

Answer 14

Ohh right!

Answer 15

Now, that is the whole process you will ALWAYS use for inverses...so does that make sense? any parts cloudy?

Answer 16

The given answers are single numbers, though.

Answer 17

*We aren't done yet ^_^

Answer 18

OH alright!

Answer 19

Remember we still have the "when x = 3" part to deal with :)

Answer 20

SOOOOOO

since we know that

\[\large y = \frac{x - 7}{4}\]

"when x = 3" what does y equal?

Answer 21

-1?

Answer 22

Indeed! :)

Answer 23

Thank you so very much!

Answer 24

Of course, Anytime! :)