Question

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

Answer 1

Answer: $f(-64)=0$

$f64)=0$

Step-by-step explanation:

The given function : $f(x)=16-x^{2/3}$

When we substitute x= -64, we get

$f(x)=16-(-64)^{2/3}$

Since , $64=4\times4\times4=4^3$

So, $-64=-4\times-4\times-4=-4^3$

That means  $f(-64)=16-(-64)^{2/3}=16-(-4^3)^{2/3}$

$=16-(-4)^2=16-(-4\times-4)=16-16=0$

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

Similarly, When we substitute x= 64, we get

$f(x)=16-(64)^{2/3}$

Since , $64=4\times4\times4=4^3$

That means  $f(64)=16-(64)^{2/3}=16-(4^3)^{2/3}$

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

i.e. $f64)=0$