class 12 maths relations and functions

If $f:$

VAVidaara Admin Asked 8d ago 0 views 0 answers
📘 Relations and Functions 2,\infty ) \to R$ be the function defined by $f(x) = {x^2} - 4x + 5$, then the range of $f$ is \begin{enumerate} \item $R$ \item $[1,\infty )$ \item $[4,\infty )$ \item $[5,\infty )$ \end{enumerate} [NCERT Exemp.Q.44,Pa MCQ 1 mark

If $f:$

Official Solution

VVidaara Team ✓ Verified solution NCERT & Exemplar

It is given that,, $f(x) = {x^2} - 4x + 5$

Let $y = {x^2} - 4x + 5$

$\Rightarrow$ $y = {x^2} - 4x + 4 + 1 = {(x - 2)^2} + 1$

$\Rightarrow$ ${(x - 2)^2} = y - 1 \Rightarrow x - 2 = \sqrt {y - 1}$

$\Rightarrow$ $x = 2 + \sqrt {y - 1}$

$\therefore y - 1 \ge 0,y \ge 1$

Range $= [1,\infty )$

View the full step-by-step solution page & related questions →

Community Answers (0)

Log in to post your own answer or join the discussion.

Discussion (0)

No comments yet — start the discussion.

← Back to all questions