Cube root means: what number multiplied by itself 3 times, will give you the number under the radical.
In this case, you start with the cube root of (-8) after you plug in (-2) into the original equation.
The cube root of (-8) = -2
To check your answer: multiply -2 times itself 3 times...

f(x) means to evaluate the function for a given number x. ("f" is just the name of the function - it could have been named g(x), or z(x) or *(x)... ).
In this case they gave you the number to evaluate this function: -7.
So simply plug the number they want you to use (-7)...

7x + 8 = 1
1) Get all numbers on one side of the equals sign & leave "x" by itself on the other side of the equals sign.
2) Think of doing opposite operations (addition is the opposite of subtraction; division is the opposite of multiplication...)
3) Begin with numbers...