Let f(x) =x^2 +2 and g(x)=2x + 1
Find and simplify each of the following bexpressions.
a)...f(4)
b)...g(a+2)
c)...(fog)(2)
To find and simplify each expression, we need to substitute the given values into the respective functions and evaluate them. Let's go step by step:
a) To find f(4), we substitute x = 4 into the function f(x) = x^2 + 2:
f(4) = (4^2) + 2 [Substituting x with 4]
= 16 + 2
= 18
Therefore, f(4) = 18.
b) To find g(a+2), we substitute x = a+2 into the function g(x) = 2x + 1:
g(a+2) = 2(a+2) + 1 [Substituting x with a+2]
= 2a + 4 + 1
= 2a + 5
Therefore, g(a+2) = 2a + 5.
c) To find (fog)(2), we first need to find g(2), and then substitute this value into f(x):
g(2) = 2(2) + 1
= 4 + 1
= 5
Now we substitute the result g(2) = 5 into f(x):
(fog)(2) = f(g(2)) = f(5) [Substituting x with 5]
= (5^2) + 2
= 25 + 2
= 27
Therefore, (fog)(2) = 27.
In summary:
a) f(4) = 18
b) g(a+2) = 2a + 5
c) (fog)(2) = 27