Find approximations of the given value
f(x)={4; 4>x
{x^2 2<x
a)f(-6)
b)f(0)
c)f(2)
d)f(4)
e)(f(6) − f(4))/(6 − 4)
I don't understand how to solve this problem.
Thank You.
To find the approximations of the given values for the function f(x), we simply need to substitute the respective values of x into the function and calculate the corresponding outputs.
a) f(-6): For x less than 4, the function is equal to 4. Therefore, f(-6) = 4.
b) f(0): Again, for x less than 4, the function is equal to 4. So, f(0) = 4.
c) f(2): For x greater than 2, the function becomes x^2. Therefore, f(2) = 2^2 = 4.
d) f(4): At x = 4, the function transitions from being equal to 4 to becoming x^2. So, f(4) = 4^2 = 16.
e) (f(6) − f(4))/(6 − 4): To find this value, we need to substitute the given values into the function and compute the result. f(6) = 6^2 = 36 and f(4) = 4^2 = 16. So, the expression becomes (36 - 16)/(6 - 4), which simplifies to 20/2. Therefore, (f(6) − f(4))/(6 − 4) = 10.
Summary:
a) f(-6) = 4
b) f(0) = 4
c) f(2) = 4
d) f(4) = 16
e) (f(6) − f(4))/(6 − 4) = 10