Question

Let f(x)=√9x and g(x) = x + 7.
What’s the smallest number that is in the domain of fog

Answer 1

f(g(x))

• √9(x+7)
• √9x+63

The smallest no for the domain is -63 as square root of a negative no not possible.

For -63

• √-63+63
• 0

Answer 2

x = -7

Explanation:

`\begin{aligned}f \circ g=f[g(x)] & = √(9(x+7))\\& = √(9)√(x+7)\\ & = 3√(x+7)\end{aligned}`

Domain = input values (x-values)

As we cannot square root a negative number, the domain is:

x ≥ -7 → [-7, ∞)

Therefore, the smallest number that is in the domain of
`f \circ g` is -7