Question

Let$f\left(x\right)=\frac{\log (1+x^2)}{x^4-26x^2+25}$.

• A. f is continuous on $[6,10]$
• B. f is continuous on $[-2,2]$
• C. f is continuous on $[-6,6]$
• D. f is continuous on $[2,4]$

Answer 1

Answer: (A), (D)

f is continuous on $[6,10]$
f is continuous on $[2,4]$

$f\left(x\right)=\frac{\log (1+x^2)}{x^4-26x^2+25}=\frac{\log (1+x^2)}{(x-5)(x+5)(x-1)(x+1)}$

This function is not defined at $x=\pm 1,\pm 5$. Everywhere else, it is continuous because it is the quotient of two continuous functions.
Therefore the function is continuous in $[6,10]$ and $[2,4]$