SOLUTION: How do u solve this problem. Given: f(x)= x + 2 and g(x) = x^2 + 2 Problem: f(g(1)) how do i do this??

Algebra ->  Rational-functions -> SOLUTION: How do u solve this problem. Given: f(x)= x + 2 and g(x) = x^2 + 2 Problem: f(g(1)) how do i do this??      Log On


   

Question 176712: How do u solve this problem.
Given: f(x)= x + 2 and g(x) = x^2 + 2
Problem: f(g(1))
how do i do this??
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
For x in g(x) substitute 1 and do the arithmetic. Take this value for g(1) and substitute for x in f(x) and do the arithmetic.

Alternatively, though I think it is a bit more work, you could substitute the expression for g(x) for the x in f(x) giving you an expression for (f◦g)(x). Then you can substitute 1 for x in the derived expression.

In general, given a function f defined by f(x) = [some expression in x], you evaluate f(a) by substituting a for x in the expression. It doesn't matter whether a is a number, some other variable, or another function definition or composite of functions.

Remember that f or g or h or some other letter is a function, f(x) or g(x) etc. is the value of the function at x. f(a), then, is the value of the function at a. Typically, things like f(x) are used to describe the general rule for the specific function whereas f(a) is used to examine the value of a particular function at a specific point, namely a.