Question

Given f(x) = the quantity of 4x plus 1, divided by 3 solve for f-1(3).

Answer 1

\[\large f(x) = \frac{4x + 1}{3}\]

We want the inverse of this...so first we make f(x) = y ...and then we switch the positions of the 'x' and 'y'

\[\large x = \frac{4y + 1}{3}\]

Now we just need to solve for 'y' again...

Any idea how to start that?

Answer 2

no clue math is not my subject at all I struggle

Answer 3

No problem :)

Alright so we have

\[\large x = \frac{4y + 1}{3}\]

We want to use algebra to solve for 'y' agan...so lets begin by multiplying both sides of this equation by 3...*because it will cancel out the '3' on the right side*

\[\large 3x = 4y + 1\]

See what I did there?

Answer 4

Yes

Answer 5

Alright...now we want to isolate the 4y...so lets subtract 1from both sides of the equation *to cancel it again on the right side*

\[\large 3x - 1 = 4y\]

The last step...is to divide everything by 4...this will cancel out the 4y on the ight leaving us with just 'y'

\[\large y = \frac{3x - 1}{4}\]

This is our inverse...now we just need to evaluate it when x = 3

Answer 6

Okay that makes sense

Answer 7

Alright..so then we have

\[\large y =\frac{3x - 1}{4}\]
\[\large y = \frac{3(3) - 1}{4}\]
\[\large y = \frac{9 - 1}{4}\]
\[\large \frac{8}{4}\]
\[\large y = \space?\]

Answer 8

y==2

Answer 9

Perfect :)

Answer 10

Thank you that makes much more sense now!

Answer 11

Anytime :)