Question

Help please -

Given the function f(x) = The quantity of 2x minus 5, divided by 3, which of the below expressions is correct?

f−1(x) = The quantity of 5 minus 2x, divided by 3.

f−1(x) = The quantity of 3x minus 5, divided by 2.

f−1(x) = The quantity of 3x plus 5, divided by 2.

f−1(x) = The quantity of negative 2x minus 5, divided by 3.

I kind of know how to solve for inverses, but not like this. Really needing some help with this one...

Answer 1

c is the ans.

Like this you do, we have been given f(x)=2x-5/3

so you can take that as also, y=2x-5/3
shift the 3 to the other side and division changes to multiplication, 3y=2x-5
now shift 5 to the other side and -ve becomes +ve, 3y+5=2x,

divide both sides by 2, so you get, 3y+5/2=x

now you can also write x as f-1(y)=3y+5/2

I just made f(x) as y to make it easier, of course there are many ways to do it.

Answer 2

At the last, you can change it back to f-1(x) and you will get the same ans as: 3x+5/2

Answer 3

Thank you so much! I was having a really hard time, and you were able to explain it in detail!

Answer 4

Remember that 3x+5, is whole divided by 2.