i need help with this problem?

Question

Explain why f(x)=x2(the 2 is the exponent)and g(x)=x(the x is under a square root sign

Answer 1

Well, the why of it is that they are defined that way. The function f(x)=xsquared means that for every value of x, f(x) is that value squared. so, f(2)=4, f(6)=36, etc. g(x) = squarerootx means that for every value of x, the function g(x) will be the square root, so g(9)=3, g(16)=4, etc. If you have a series of numbers that form a pattern based on a particular function, you can define that function by the series. So, for instance, if you have a series that goes 1,2,3,4,5,6,7,8,9,etc., then f(x)=x+1. If the series was 2,5,10,17,26, etc., then f(x)=xsquared + 1. The function designations 'f' (as in f(x)) or 'g' are purely arbitrary based on custom. You could equally well write "the function Q(z)=z/5 + 21z"