Which would be the inverse of this:

Question

Let f(x)=(x+3)(2x-5)

f^ (-1) x = (5x - 3)/ (2x + 1)

f^ (-1) x = (5x + 3)/ (2x - 1)

Answer 1

Could you check if there wasn't a typo, namely,
"Let f(x)=(x+3)/(2x-5)... "
If that's the case, it's the second response.
To double check,
let g(x)=f^-1(x)=(5x+3)/(2x-1)
Evaluate
f(g(x))
= ((5x+3)/(2x-1)+3)/((2(5x+3))/(2x-1)-5)
= x

Answer 2

Let y = f(x)

y = (x + 3)/ (2x - 5)

Switch x and y.

x = (y + 3)/ (2y - 5)

Multiply both sides by (2y - 5).

2xy - 5x = y + 3

Subtract 3 from both sides.

2xy - 5x - 3 = y

Subtract 2xy from both sides.

-5x - 3 = -2xy + y

Factor the right side.

-5x - 3 = y (-2x + 1)

Divide both sides by (-2x + 1).

(-5x - 3)/ (-2x + 1) = y

(5x - 3)/ (2x + 1) = y

Now we replace y with the inverse function notation: f^ (-1) x.

f^ (-1) x = (5x + 3) / (2x - 1)

This my work to reflect the answer. Is it correct? Thanks!

Answer 3

Yes, the calculation is correct.

Note: You may not have noticed that you omitted the division sign in the initial post.

Answer 4

Thanks for pointing that out!

Answer 5

You're welcome!