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)
f(4) ?
just replace the x with 4 in the expressio
g(a+2), same thing, replace x with a+2 in g(x)
= 2(a+2) + 1
= 2a + 5
fog(x) means f(g(x))
so g(2) = 5
then f(5) = 25 + 2 = 27
To find the values of the given expressions, we need to substitute the values of x into the respective functions and simplify.
a) To find f(4), we substitute x = 4 into the function f(x) = x^2 + 2:
f(4) = (4)^2 + 2
= 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
= 2a + 4 + 1
= 2a + 5
Therefore, g(a+2) = 2a + 5.
c) To find (fog)(2), we need to first find g(2) and then substitute the result into the function f(x).
First, let's find g(2):
g(2) = 2(2) + 1
= 4 + 1
= 5
Now, substitute the value of g(2) into the function f(x):
(fog)(2) = f(g(2))
= f(5)
Applying f(x) = x^2 + 2:
(fog)(2) = (5)^2 + 2
= 25 + 2
= 27
Therefore, (fog)(2) = 27.