Solve the problem.
-Given $f ( x ) = \frac { x - 7 } { x + 5 }$, find all values for $x$ for which $f ( x )

Question

Solve the problem.
-Given $f ( x ) = \frac { x - 7 } { x + 5 }$, find all values for $x$ for which $f ( x ) < 0$.
A) $( - \infty , - 5 ) \cup ( 7 , \infty )$
B) $( 7 , \infty )$
C) $( - \infty , - 5 )$
D) $( - 5,7 )$

Quizplus · Accepted Answer

The function $f(x) = \frac{x - 7}{x + 5}$ is negative when the numerator and denominator have opposite signs. This happens when $x < -5$ (denominator negative, numerator positive) or when $-5 < x < 7$ (denominator positive, numerator negative). However, for $x < -5$, the numerator is also negative, making the fraction positive. Thus, the correct interval is $(-5, 7)$.

Solve the Problem f(x)=x−7x+5f ( x ) = \frac { x - 7 } { x + 5 }f(x)=x+5x−7​

Solve the Problem $f ( x ) = \frac { x - 7 } { x + 5 }$