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

The Correct Option is C

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)