Sets, Relations & Functions
Domain of Logarithmic Function — Base and Argument Conditions
nta_pyq_2026_jan
Grade None
Question:
If the domain of the function $f(x)=\log_{(10x^2-17x+7)}(18x^2-11x+1)$ is $(-\infty,a)\cup(b,c)\cup(d,\infty)-\{e\}$, then $90(a+b+c+d+e)$ equals:
Step-by-Step Solution
Key Concept: Conditions: (i) Base $>0$: $10x^2-17x+7>0\Rightarrow(x-1)(10x-7)>0\Rightarrow x<\tfrac{7}{10}$ or $x>1$. (ii) Base $\neq1$: $x=\tfrac{1}{2}$ or $x=\tfrac{6}{5}$. (iii) Argument $>0$: $18x^2-11x+1>0\Rightarrow(x-\tfrac{1}{9})(x-\tfrac{1}{2})\cdot18>0\Rightarrow x<\tfrac{1}{9}$ or $x>\tfrac{1}{2}$.
$90(a+b+c+d+e)=316$.
Correct Answer: 3