Question

If f(x) = 9x – 6 and g(x) g(x) = VX - 4 which statement is true?

Answer 1

To solve this question, we need to perform the composition of these two functions.

Then, we have:

`f\circ g\Rightarrow f(g(x))=9\cdot(\sqrt[]{x-4})-6`

And this is equivalent to:

`f\circ g=9\sqrt[]{x-4}-6`

The domain of this function, that is, the values for which this function is Real and is defined, is given by the values for which the radical part of the square root is greater or equal to 0:

`x-4\ge0\Rightarrow x\ge4`

Then, the domain for this composition of functions is for values greater or equal to 4. Therefore, 1 IS NOT in the domain of the composition of both functions.

Hence, the correct answer is 1 is not in the domain of f o g.