If $f(x)=\left\{\begin{matrix}\frac{x^2+

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Relations and Functions

Question:

If $f(x)=\left\{\begin{matrix}\frac{x^2+3x+λ}{x-1}&;&x≠1\\4&;&x=1\end{matrix}\right.$

Options:

$λ = –4$

$λ = 4$

$λ = –5$

none of these

Correct Answer:

none of these

Explanation:

$x^2 + 3x + λ$ must be zero at x = 1

So, $λ = –4$

But $\underset{x→1}{\lim}\frac{x^2+3x-4}{(x-1)}=5$ . So no value of λ exist.