Question

Let f(x) = square root of 7x and g(x) = x - 2. What's

the smallest number that is in the domain of
fºg?

Answer 1

The smallest number that is in the domain is 2

Explanation:

we have

`f(x)=√(7x)`

`g(x)=x-2`

we know that

`fog(x)=f(g(x))`

Substitute the variable x by the function g(x) in the function f(x)

so

`f(g(x))=√(7(x-2))`

`f(g(x))=√(7x-14)`

Remember that the radicand must be greater than or equal to zero

`7x-14\geq 0`

Solve for x

Adds 14 both sides

`7x\geq 14`

Divide by 7 both sides

`x\geq 2`

The domain is the interval [2,∞)

therefore

The smallest number that is in the domain is 2