If f(x) =-2+8 and g(x) = square root of x+9 which statement is true
1 answer:
The statement that -6 is in the domain of f(g(x)) is true
<h3>Complete question</h3>If f(x) = -2x + 8 and g(x) = , which statement is true?
- -6 is in the domain of f(g(x))
- -6 is not in the domain of f(g(x))
We have:
f(x) = -2x + 8
Start by calculating the function f(g(x)) using:
f(g(x)) = -2g(x) + 8
Substitute
Set the radicand to at least 0
Subtract 9 from both sides
This means that the domain of f(g(x)) are real numbers greater than or equal to -9. i.e. -9, -8, -7, -6, ...........
Hence, the statement that -6 is in the domain of f(g(x)) is true
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(See the attached plot; the given surface is orange, (0, 0, 8) is the black point, the tangent plane is blue, and the red line is the normal at this point)
