Question

Please giving 20 points!!!

Which of the following functions satisfies these two characteristics: f(0) = 0, f(2) = π *
f(x) = -2 sec(x)
f(x) = 7sin(x/4 - 1/29)
f(x) = π cos(πx)
f(x) = 2π cos(x - π/2)

Answer 1

we choose f(x) = π cos(πx)

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
`(1)/(cos(o))` = -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)