How do you go about finding the Domain?

[Josilyn08]

Problem #1: F(x)= 7 over 6x-13



Problem #2: F(x)= x+3 over x^2-5x-24



Problem #3: F(x)= Square Root of -3x+5

 

[DrSteve]

For the first 2, the denominator cannot be zero. For example,

\(\displaystyle 6x-13=0 \Leftrightarrow 6x=13 \Leftrightarrow x=\frac{13}{6}\)

So the domain is all x except \(\displaystyle x=13/6\).


For the last one, the expression under the square root must be greater than or equal to zero.

\(\displaystyle -3x+5\geq 0 \Leftrightarrow -3x\geq -5 \Leftrightarrow x\leq \frac{5}{3}\).