Question

Given f(x) = 4-x² and (f - g)(x)=-x²+x+2, find the function g.

Answer 1

`{ \rm{f(x) = 4 - {x}^(2) }}`

`{ \rm{(f - g)(x) = - {x}^(2) + x + 2}}`

- From functions;

`{ \boxed{ \tt{(f - g)(x) = f(x) - g(x)}}} \\ \\ { \rm{ - {x}^(2) + x + 2 = (4 - {x}^(2) ) - g(x) }} \\ \\ { \rm{g(x) = (4 - {x}^(2)) + {x}^(2) - x - 2 }} \\ \\ { \boxed{ \rm{g(x) = 2 - x}}}`

Answer 2

• g(x) = 2 - x

Explanation:

Given

• f(x) = 4 - x²,
• (f - g)(x) = - x² + x + 2.

Find

• g(x)

Solution

We know that:

• (f - g)(x) = f(x) - g(x)

Use the given to find the missing function:

• g(x) = f(x) - (f - g)(x)

• g(x) =
• 4 - x² - (- x² + x + 2) =
• 4 - x² + x² - x - 2 =
• 2 - x