To find the domain of this function why don't we consider the numerator?
In the function f(x) = (4-x)/2+log base 2 of x
to find the domain we set the denominator different from zero and x>0 cause of the log but why dont we set 4-x different from zero? please help me clarify this doubt, thanks in advance
1 Answer
Let $f(x)=\frac{4-x}{2}+\log_2 ^{x}$.
Since $\log_2 ^{x}$ is not defined for $x\leq 0$, we must have $x>0$. On the other hand $\frac{4-x}{2}$ is defined for all $x$ (note that there is no division by zero). So the domain of $f$ is $x>0$ or
\[(0,\infty).\]
You do not set $4-x$ to be zero, because $4-x$ in not in the denominator. It is fine to devide 0 by any number, but we should avoid dividing by zero. In the expression $\frac{4-x}{2}$ you never divide by zero.
Daniel90
443
Join Matchmaticians Affiliate Marketing
Program to earn up to a 50% commission on every question that your affiliated users ask or answer.
- 1 Answer
- 299 views
- Pro Bono
Related Questions
- Are my answers correct
- Convergence of integrals
- Rouche’s Theorem applied to the complex valued function $f(z) = z^6 + \cos z$
- A bicycle with 18in diameter wheels has its gears set so that the chain has a 6 in. Radius on the front sprocket and 4 in radius on the rear sprocket. The cyclist pedals at 180 rpm.
- Find the exact form (Pre-Calculus)
- Sinusoidal function question help
- True-False real analysis questions
- Calculus - functions, limits, parabolas
Domain means where (= for which x) the function is defined (= where it can be computed). The fraction (4-x)/2 can be computed for any x, no problem when it's negative or zero. But the second tem uses the log function, which is only defined for positive arguments, but not when x <= 0. (Check the graph of log(x) - you can ask google "plot log(x)" : it goes to minus infinity when x approaches 0 from the right.) So we need x > 0. (The sum of the two terms is defined whenever both are defined.)