Question

If $f:R\to R$ given by $f\left(x\right)=3x-4$ then $f^{-1}\left(5\right)$ and $f^{-1}(-5)$ are

• A. $3,\frac{-1}{3}$
• B. $2,\frac{-1}{2}$
• C. $5,\frac{-1}{5}$
• D. $0,0$

Answer 1

Answer: (A)

$3,\frac{-1}{3}$

Given that:

$f:R\to Randf\left(x\right)=3x-4$

Put $f\left(x\right)=y$

$y=3x-4$

$x=\frac{y+4}{3}$

Put $x=f^{-1}\left(y\right)$

$f^{-1}\left(x\right)=\frac{x+4}{3}$

So,

$f^{-1}\left(5\right)=\frac{5+4}{3}\Rightarrow f^{-1}\left(5\right)=3$

and

$f^{-1}(-5)=\frac{-5+4}{3}\Rightarrow f^{-1}(-5)=\frac{-1}{3}$

So answer is $3,\frac{-1}{3}$