Question

f f(x)= 4x?1 if ?4?x?4 and x3?4 if 4<x?5 ?, ?find: (a)? f(0), (b)? f(1), (c) ?f(44?), (d) f(5)

Answer 1

Given,

f(x) = 4x-1 if  ?4?x?4...........(1)

f(x) = x³-4 if 4<x?5........(2)

a) f(0), as 0 lies in 1st interval,

we use, f(x) = 4x-1

implies, f(0) = 4(0)-1 = -1

f(0) = -1

b) f(1), as 1 lies in 1st interval,

we use, f(x) = 4x-1

implies, f(1) = 4(1)-1 = 3

f(1) = 3

c) f(44) ........ I am asuuming there is an error in question as the function is not defined for x =44. So,

taking f(4) which is under 1st intervel of ?4?x?4

So, f(4) = 4X4 -1 = 15

d) f(5) , x = 5 is under the interval 4<x?5.

So, f(x) =  x³-4

f(5) =  5³-4 = 125-4 = 121

f(5) = 121