Question

The domain of the real valued function $f(x)=\dfrac{√(x2−7x+6)}{√(​x2−4​+1)}$ is

• A. R-[-6,-2)
• B. R-[-6,-2)
• C. R-[-6,2)
• D. R-[-2,6)
• E. R-(-2,6]

Answer 1

Answer: (C)

R-[-6,2)

Answer 2

Given that

$f(x)=\dfrac{√(x2−7x+6)}{√(​x2−4​+1)}$​

[Note: The domain of a function is the set of all possible input values (values of $x$) for which the function is valid.]

According to the question we can write,

For, $x^{2}−4x^{2}−4: x^{2}−4≥0$
This inequality holds true for $−2≤x≤2$ as $x^{2}$ is non-negative in this interval.

Similarly ,for $x^{2}−7x+6 : x^{2}−7x+6>0$
This inequality holds true for $x<−6$ and $x>2$, as $x^{2}−7x+6x+6$ is positive in these intervals.

We can get the domain by combining the two terms as:

The function is defined for $x$ in the intervals $(−2,2), (−∞,−6) , (2,∞)$.

now domain, $D=(−∞,−6)∪(−2,2)∪(2,∞)$.

So, the correct option for the domain of the function is $D$ is $R−[−6,2)$. (_Ans)