Express the function F(x)=(x^2-5)^2 in the form fog

Question

Express the function F(x)=(x^2-5)^2 in the form fog

f(x)=

g(x)=

Answer 1

F(x) as a composite function fog is a function g(x) within a function f(y). Look at the parentheses to see the demarcation of the two functions: ( x^2-5 ) is inside the parentheses, and the exponent 2 is outside the parentheses, that is, ( )^2. fog means that f(y) is the outside function and g(x) is the inside function, that is, g(x) is the argument of f(y) or fog(x) = f(g(x)). So, y= g(x) = x^2-5 and f(y) = (y)^2. Since we usually write both f and g as functions of x, we have f(x) = x^2 and g(x) = x^2-5. Note that the x^2 of f(x) is not meant to be the same as the x^2 in g(x).