Question

What is the domain of the function y=3√6x+42 A. x ≥ 0 B. x ≤ 7 C. x ≥ –6 D. x ≥ –7

Answer 1

Answer:  The correct option is (D) $x\geq -7.$

Step-by-step explanation:  We are given to find the domain of the following function:

$y=3\sqrt{6x+42}~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

The domain of a function y = f(x) is the set of all possible x-values which will make the function defined or will output real y-values.

That is, for the function (i), the domain will be given by all those values of x for which $3\sqrt{6x+42}$ is real.

Now, the values of y will be real only if the expression under square root is greater than or equal to 0.

Therefore, the domain of function (i) is

$\sqrt{6x+42}\geq0\\\\\Rightarrow 6x+42\geq 0\\\\\Rightarrow 6x\geq -42\\\\\Rightarrow x\geq -\dfrac{42}{6}\\\\\Rightarrow x\geq -7.$

Thus, the domain of the given function is $x\geq -7.$

Option (D) is CORRECT.

Answer 2

The domain of  the function:
y = 3 √ ( 6 x + 42 )
6 x + 42 ≥ 0
6 x ≥ - 42
x ≥ - 42 : 6
x ≥ - 7
Answer:
The domain is D ) x ≥ - 7