Let f: mathbbR → mathbbR defined as f(x) = 2x - 3. Find f⁻¹(x) domain and range of f⁻¹(x)

Let $f: \mathbb{R} \to \mathbb{R}$ defined as $f(x) = 2x - 3$. Find

(i)[1]

$f^{-1}(x)$

(ii)[1]

domain and range of $f^{-1}(x)$

Answer

Answer (i)

Let $y = 2x - 3$. Then $x = \frac{y+3}{2}$.

Final answer: $\frac{x+3}{2}$

Answer (ii)

$f$ is one to one and onto $\mathbb{R}$, so $f^{-1}(x) = \frac{x+3}{2}$ is defined for every real $x$ and takes every real value.

Final answer: Domain $= \mathbb{R}$, range $= \mathbb{R}$