Let f: R → R be the function defined by f (x) = 3x – 5 ∀ x ∈ R. Then write f ^–1.

Question

Question

\(\frac{{x + 5}}{3}\)
\(\frac{{y + 5}}{3}\)
\(\frac{{x - 5}}{3}\)
\(\frac{{x + 3}}{5}\)
None of these

Answer 1

CONCEPT:

A function f: X → Y is defined to be invertible, if there exists a function g: Y → X such that g o f = I_x and

f o g = I_Y. The function g is called the inverse of f and is denoted by f ^–1.

For calculation of inverse of any function, it should be arranged in the terms of x = f(y) and then every y should be replaced with x.

CALCUATIONS:

Given that f (x) = 3x – 5 = y (say),

then 3x = y + 5 ⇒ \(x = \frac{{y + 5}}{3}\)

Hence \(x = {f^{ - 1}}\left( y \right) = \frac{{y + 5}}{3}\) ⇒ \({f^{ - 1}}\left( x \right) = \frac{{x + 5}}{3}\)