Question

Consider the following function.f(x) = 16 − x2/3Find f(−64) and f(64).

Answer 1

Answer:
`f(-64)=0`

`f64)=0`

Explanation:

The given function :
`f(x)=16-x^(2/3)`

When we substitute x= -64, we get

`f(x)=16-(-64)^(2/3)`

Since ,
`64=4*4*4=4^3`

So,
`-64=-4*-4*-4=-4^3`

That means
`f(-64)=16-(-64)^(2/3)=16-(-4^3)^(2/3)`

`=16-(-4)^2=16-(-4*-4)=16-16=0`

i.e.
`f(-64)=0`

Similarly, When we substitute x= 64, we get

`f(x)=16-(64)^(2/3)`

Since ,
`64=4*4*4=4^3`

That means
`f(64)=16-(64)^(2/3)=16-(4^3)^(2/3)`

`=16-(4)^2=16-16=0`

i.e.
`f64)=0`