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Question: If \(f:R \rightarrow R\) is given by \(f(x) = 3x - 5,\) then \(f^{- 1}(x)\)...

If f:R→Rf:R \rightarrow R is given by f(x)=3x−5,f(x) = 3x - 5, then f−1(x)f^{- 1}(x)

A

Is given by 13x−5\frac{1}{3x - 5}

B

Is given by x+53\frac{x + 5}{3}

C

Does not exist because f is not one-one

D

Does not exist because f is not onto

Answer

Is given by x+53\frac{x + 5}{3}

Explanation

Solution

Clearly, f:R→Rf:R \rightarrow R is a one-one onto function. So, it is invertible.

Let f(x)=y.f(x) = y. then, 3x−5=y⇒x=y+53⇒f−1(y)=y+53.3x - 5 = y \Rightarrow x = \frac{y + 5}{3} \Rightarrow f^{- 1}(y) = \frac{y + 5}{3}. Hence, f−1(x)=x+53.f^{- 1}(x) = \frac{x + 5}{3}.