Question

The function, f is defined by 𝑓: 𝑥 → 2𝑥−3
𝑥
, 𝑥 ≠
0. Find 𝑓−1
A. 3
𝑥−2
B. 3
2−𝑥
C. 2
𝑥−3
D. 2
3−𝑥

Answer 1

Since they stipulated that 𝑥 ≠0, I assume they meant
f(x) = (2x-3)/x = 2 - 3/x
so the inverse is B: y = 3/(2-x)

Answer 2

To find the inverse of f, we need to solve for x in terms of f(x).

Starting with f(x) = 2x - 3:

f(x) = y = 2x - 3

Add 3 to both sides:

y + 3 = 2x

Divide by 2:

x = (y + 3)/2

So the inverse function is:

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

Substituting y back in for x:

f^-1(y) = (y + 3)/2

Therefore, the answer is A) 3/(x-2).

Answer 3

You are correct, if we interpret the function as f(x) = (2x-3)/x for x ≠ 0, then the inverse function would be y = 3/(2-x), which corresponds to answer choice B. Thank you for catching that!