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Find the root of the function [tex]f(x)=\frac{1}{x+3}[/tex].

A. None
B. [tex]x = -3[/tex]
C. [tex]x = -2[/tex]
D. [tex]x = -4[/tex]


Sagot :

To find the root of the function [tex]\( f(x) = \frac{1}{x+3} \)[/tex], we need to solve for [tex]\( x \)[/tex] such that [tex]\( f(x) = 0 \)[/tex].

First, let's set the function equal to zero and analyze the equation:
[tex]\[ f(x) = \frac{1}{x+3} = 0 \][/tex]

This means we need to solve:
[tex]\[ \frac{1}{x+3} = 0 \][/tex]

For a fraction to equal zero, its numerator must be zero. However, the numerator in our fraction is a constant 1, and it will never be equal to zero no matter what value [tex]\( x \)[/tex] takes. This fraction [tex]\( \frac{1}{x+3} \)[/tex] is undefined when the denominator is zero:
[tex]\[ x + 3 = 0 \\ x = -3 \][/tex]

At [tex]\( x = -3 \)[/tex], the function is undefined, not zero. Therefore, the function [tex]\( f(x) = \frac{1}{x+3} \)[/tex] does not have any real roots because there is no value of [tex]\( x \)[/tex] that can satisfy the equation [tex]\( \frac{1}{x+3} = 0 \)[/tex].

Given the choices:
A. none
B. [tex]\( x = -3 \)[/tex]
C. [tex]\( x = -2 \)[/tex]
D. [tex]\( x = -4 \)[/tex]

The correct answer is:
A. none