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

Answer:

$f(-1) = 3$

$f(2) = 6$

$f(12) = 41$

Step-by-step 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

$f(12) = 4(12) - 7$  

$f(12) = 48 - 7$

$f(12) = 41$