Use the function to evaluate the indicated expressions and simplify.

Question

f(x) = x + 8

 

 

1. f(x²) =

 

2. (f(x))² =

Answer 1

f(x) = x + 8

1.f(x²)=?

Substitute x²  into the function:

1.  f(x²) = x² + 8

Substitute f(x) into the function and square the result:

2.(f(x))²

 (f(x))² = (x + 8)² = x² + 16x + 64

Hope so it will help you

Answer 2

Adding to the nice explanations from Phillip and David, and in light of your other posted problem and likely topics about composition of functions, we can view

 

h(x) = x^2 as another function and say that

 

f(x^2) = f(h(x))

 

and [f(x)]^2 = h(f(x))

 

David's verbal explanation of the difference between square feet and feet, squared is important to help illustrate the differences between these two compositions, and how the order in which we compose functions together is (in general) VERY important, as composition of functions is NOT a commutative operation (for two arbitrary functions).

Answer 3

It is sometimes difficult to explain the difference between something that is “5 feet squared” and something that is “5 square feet.”  Thank goodness for parentheses.  I’d say the first one as “(five feet) squared.”

It happens so often  --  we use x and y and z and … so often that we have trouble remembering what they mean, so we have to keep a catalog of information to help us remember.  Here, the “function of x” is the catalog entry that will be used for (potentially many) situations, some of them actually use “x” (another one) or even “function of x” (to mean our x !).

For this problem, the x in the function may be replaced by anything you want, including something that has (another) x in the expression, so

     F(x²)  =   (x²) + 8              [ replace function’s x with point 1’s x²  ]

And

    (  f(x) )² =  (x+8)²    [ replace function’s x with point 2’s f(x), which is function’s x+8 ]

                     =  x² + 16x + 64   (this may not look like simplified, but it is a more standard form

Answer 4

f(x) = x + 8

1.  f(x²) = x² + 8
2.  (f(x))² = (x + 8)² = x² + 16x + 64