Question

Given f(x) = x2-2 and g(x) = sqrt x find f(g(2))

Answer 1

The value of
`f(g(2))` is 0

Explanation:

Given:

`f(x) = x^2-2` and
`g(x) = √(x)`

we have to find the
`f(g(2))`.

first find
`g(2)`

Put x =2 in g(x) we have;

`g(2) = √(2)`

Now;

`f(g(2))=f(√(2))=(√(2))^2-2 = 2-2 = 0`

Therefore, the value of
`f(g(2))` is 0

Answer 2

`\boxed{\boxed{f\bigg(g(2)\bigg)=0}}`

Explanation:

`f(x)=x^2-2,\ g(x)=√(x)\\\\Domain:\\D_f:x\in\mathbb{R}\\\\D_g:x\geq0\\\\f(g(x))=\left(√(x)\right)^2-2=x-2`

`Used:\\\\(√(a))^2=a`

`f(g(2)):\\\text{Put x = 2 to the equation of the function:}\\\\f(g(2))=2-2=0`