Question

Given g(x)=Squareroot x-4 and h(x)=2x-8, what is g(h(10))

Answer 1

Explanation:

Answer 2

`g(h(10)) = 2\sqrt 2`

Explanation:

Given

`g(x) = \sqrt {x - 4`

`h(x) = 2x - 8`

Required

`g(h(10))`

First, calculate
`g(h(x))`

We have:

`g(x) = \sqrt {x - 4`

This gives:

`g(h(x)) = \sqrt {h(x) - 4`

Substitute
`h(x) = 2x - 8`

`g(h(x)) = \sqrt {2x - 8 - 4`

`g(h(x)) = \sqrt {2x - 12`

Substitute
`x = 10`

`g(h(10)) = \sqrt {2*10 - 12`

`g(h(10)) = \sqrt {20 - 12`

`g(h(10)) = \sqrt {8\\`

Split

`g(h(10)) = \sqrt {4} * \sqrt 2`

This gives

`g(h(10)) = 2\sqrt 2`