In the question, the input of the function is that value which you'll insert in place of x, and whatever answer you get is the output.
The function is described as a machine, where you can input values and get answers called output values.
In this instance the input value into the machine is 8, that is wherever you have an x, change it into 8. Therefore we now have,
f(x) = x² + 7
f(8) = 8² + 7
f(8) = 64 + 7
f(8) = 71
So when the input is 8, the output from the machine is 71
For the other machine, the input into the machine is -10. The machine itself is given as |x + 6|
The two lines that bounds the expression means your answer must be in "absolute" value or must be a positive value.
The output can now be derived as;
f(x) = x + 6
f(-10) =-10 + 6
f(-10) = -4
f(-10) = 4 (Absolute Value)
