f(x) = 2x-8 and g(x) = sqrt x-5 find (fog)(30)
(f◦g)(x) = f(g(x)) = 2g-8 = 2√(x-5) - 8
so,
(f◦g)(30) = 2√25 - 8 = 2*5 - 8 = 2
or,
f(g(30)) = f(√25) = f(5) = 2*5-8 = 2
To find (fog)(30), which represents the composition of two functions f(x) and g(x), we need to apply the function g(x) to the value of 30, and then pass the result to the function f(x).
First, let's find g(30):
g(x) = sqrt(x-5)
Replace x with 30:
g(30) = sqrt(30-5)
Simplify:
g(30) = sqrt(25)
g(30) = 5
Now, we have g(30) = 5.
Next, we will substitute this result into f(x):
f(x) = 2x - 8
Replace x with g(30):
f(g(30)) = 2 * g(30) - 8
Replace g(30) with 5:
f(g(30)) = 2 * 5 - 8
Simplify:
f(g(30)) = 10 - 8
f(g(30)) = 2
Therefore, (fog)(30) = 2.