Question

Given f(x) = -x + 6 and g(x) = f(x + 3) write an equation for function g

Answer 1

Function Composition:
`\( g(x) = f(x + 3) \)`

Given:

`\[f(x) = -x + 6\]`

To find
`\( g(x) \)`, we substitute
`\( x \)` with
`\( x + 3 \)` in
`\( f(x) \)`:

`\[g(x) = f(x + 3) = -(x + 3) + 6\]`

Simplifying the equation:

`$\begin{align*}g(x) &= -x - 3 + 6 \\g(x) &= \boxed{3 - x}\end{align*}$`

Thus, the equation for the function
`\( g(x) \)` is
`\( g(x) = 3 - x \)`.