Question

- 2x

f(x)= x +4,
4x - 7
XS-10
- 10 X2
20. Use the piecewise function to evaluate points f(-1), f(2), and f(12).
O A. f(-1) = 3, f(2) = 1, and f(12) = 41
B. f(-1) = 3, f(2) = 6, and f(12) = 41
O C. f(-1) = 2. f(2) = 1, and |(12) = 41
D. f(-1) = 2. f(2) = 6, and f(12) = 41

Answer 1

`f(-1) = 3`

`f(2) = 6`

`f(12) = 41`

Explanation:

Given

The piece wise function can be split to:-

`f(x) = -2x`
`x\leq -10`

`f(x) = x + 4`
`-10<x\leq 2`

`f(x) = 4x - 7`
`x> 2`

Required

f(-1), f(2) and f(12)

To solve for each of these functions, we first check the range they fall into, then we execute the corresponding function

Solving f(-1)

-1 is within the range of
`-10<x\leq 2`

Hence; we make use of
`f(x) = x + 4`

Substitute -1 for x

`f(-1) = -1 + 4`

`f(-1) = 3`

Solving f(2)

2 is within the range of
`-10<x\leq 2`

Hence; we make use of
`f(x) = x + 4`

Substitute 2 for x

`f(2) = 2 + 4`

`f(2) = 6`

Solving f(12)

12 is within the range of
`x> 2`

Hence; we make use of
`f(x) = 4x - 7`

Substitute 12 for x

`f(12) = 4(12) - 7`

`f(12) = 48 - 7`

`f(12) = 41`