Question

Please explain how to solve the problem.

Answer 1

Part 1)
`f(125)=6`

Part 2)
`f(-64)=-3`

Explanation:

we have

`f(x)=\sqrt[3]{x} +1`

Part 1) Find f(125)

we know that

f(125) is the value of the function f(x) when the value of x is equal to 125

so

For x=125

substitute in the function

`f(125)=\sqrt[3]{125} +1`

Remember that

`125=5^(3)`

substitute

`f(125)=\sqrt[3]{5^(3)} +1`

Applying the power of rule

`\sqrt[3]{5^(3)}=(5^(3))^{(1)/(3)}= (5)^{3*(1)/(3)}=5`

substitute

`f(125)=5 +1=6`

Part 2) Find f(-64)

we know that

f(-64) is the value of the function f(x) when the value of x is equal to -64

so

For x=-64

substitute in the function

`f(-64)=\sqrt[3]{-64} +1`

Remember that

`-64=-4^(3)`

substitute

`f(-64)=\sqrt[3]{-4^(3)} +1`

Applying the power of rule

`\sqrt[3]{-4^(3)}=(-4^(3))^{(1)/(3)}= (-4)^{3*(1)/(3)}=-4`

substitute

`f(-64)=-4 +1=-3`