Theory of Intelligence
11TH•Mathematics•Functions And Graphs•Question 1

Overview

Given that:

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Given:

f(x)=2x+3f(x) = \sqrt{2x + 3}

Substitute x=−3x = -3:

f(−3)=2(−3)+3=−6+3=−3∉R\begin{aligned} f(-3) &= \sqrt{2(-3) + 3} \\ &= \sqrt{-6 + 3} \\ &= \sqrt{-3} \notin \mathbb{R} \end{aligned}

Since the square root of a negative number is undefined in real numbers:

f(−3) is not defined in R\boxed{f(-3) \text{ is not defined in } \mathbb{R}}

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