Question

If $f:IR\to IR$ is defined by $f\left(x\right)=2x+3$, then $f^{-1}\left(x\right)$

• A. Is given by $\frac{x-3}{2}$
• B. Is given by $\frac{1}{2x+3}$
• C. Does not exist because 'f' is not injective
• D. Does not exist because 'f' is not surjective

Answer 1

Answer: (A)

Is given by $\frac{x-3}{2}$

$f:IR\to IR$

$f\left(x\right)=2x+3$

$\Rightarrow x=\frac{f\left(x\right)-3}{2}$

i.e. $f^{-1}x=\frac{x-3}{2}$