Question

Let f(x) = V10 - x - x. Find x such that f(x) = 2.

f(1) = 2
f(2) = 2
f(3) = 2
f(4) = 2

Answer 1

`f(1)=2`

Explanation:

Given:

`f(x)=√(10-x)-x`

`f(x) =2`

`√(10-x)-x=2\\√(10-x)=x+2`

Squaring both sides, we get

`(√(10-x))^(2)=(x+2)^(2)\\10-x=x^(2)+4+4x\\x^(2)+4x+x+4-10=0\\x^(2)+5x-6=0\\(x-1)(x+6)=0\\x=1\textrm{ or }x=-6`

Therefore, the possible values of
`x` for which
`f(x)=2` are -6 and 1.

Therefore,
`f(1)=2`