Evaluate for the indicated value of the independent variable.

Question

If f(x)=4x-2 and x(t)=√(t+2), find f(x(7))

Answer 1

f(x(7)) is just a function of a function.
 
First, the independent variable is t and the function is x(t),
      x(t)=√(t+2)

For t=7 that is:                  [given value of t=7; "find f(x(7))"]
  x(7) = √(7+2)                [substitute 7 for t]
  x(7) = √9

  x(7) = 3             [note: ±3; two answers means x(t) is not a function,

                            so, we take only x(7)=3]
 
Now, the function f(x)= 4x - 2 transforms x(t):
      f(x(7)) = f(3) = 4(3) - 2 = 10