Answer:
we choose f(x) = π cos(πx)
Step-by-step explanation:
Given the information:
- f(0) = 0
- f(2) = π
Let analyse all possible answers;
1/ f(x) = -2 sec(x)
when x= 0 we have: f(0) = -2 sec(0) = -2 = -2 wrong
2. f(x) = 7sin(x/4 - 1/29)
when x= 0 we have: f(0) =7sin(0/4 - 1/29) = 7sin(-1/29) = -0.00421 wrong
3. (x) = π cos(πx)
when x= 0 we have: f(0) = πcos(π0) = cos(0) = π0 = 0
when x= 2 we have: f(2) = πcos(π2) = πcos(0) = π
True
4. f(x) = 2π cos(x - π/2)
when x= 0 we have: f(0) = 2π cos(0 - π/2) = 2π cos(-π/2) = 0
when x= 2 we have: f(2) =2π cos(2 - π/2) = 2π0.034 = 0.0697π Wrong
So we choose f(x) = π cos(πx)