Sets, Relations & Functions
Range of Reciprocal Function
nta_pyq_2024_apr
Grade 11
Question:
Let $f(x)=\dfrac{1}{7-\sin5x}$ be a function defined on $\mathbb{R}$. Then the range of the function $f(x)$ is equal to:
$\left[\dfrac{1}{7},\dfrac{1}{6}\right]$
$\left[\dfrac{1}{8},\dfrac{1}{5}\right]$
$\left[\dfrac{1}{7},\dfrac{1}{5}\right]$
$\left[\dfrac{1}{8},\dfrac{1}{6}\right]$
Step-by-Step Solution
Key Concept: $\sin5x\in[-1,1]\Rightarrow7-\sin5x\in[6,8]\Rightarrow f(x)\in[1/8,1/6]$.
Range $=\left[\frac{1}{8},\frac{1}{6}\right]$.
Correct Answer: 4