Question

If f(x) = 5x - 3, then f^-1(x) is ______ 

विकल्प

• `1/(5x - 3)`

• Is given by `(x + 3)/5`

• Does not exist because f is not one-one

• Does not exist because f is not onto

Answer 1

If f(x) = 5x - 3, then f^-1(x) is `underline("given by" (x + 3)/5)`.

Explanation:

Let f(x) = y ⇒ x = `f^-1(y)`

Now, y = 5x - 3

⇒ x = `(y + 3)/5`

⇒ `f^-1(y) = x = (y + 3)/5`

∴ `f^-1(x) = (x + 3)/5`

Also, f is one-one and onto, so f^-1 exists and is given by `f^-1(x) = (x + 3)/5`.