Given function:
[tex]f(x)=4 x^{3}=c[/tex]
To find:
The input if the output is 32.
The output if the input is 4.
Solution:
Input is x and output is c.
Substitute c = 32 in f(x).
[tex]4 x^{3}=32[/tex]
Divide by 4 on both sides, we get
[tex]x^{3}=8[/tex]
[tex]x^{3}=2^3[/tex]
Taking cube root on both sides.
[tex]x=2[/tex]
The input is 2 if the output is 32.
Substitute x = 4 in f(x).
[tex]4 (4)^{3}=c[/tex]
[tex]4 (64)=c[/tex]
[tex]256=c[/tex]
The output is 256 if the input is 4.
