Answer
(fg)(5) + f(4) = 191
Work Step by Step
The notation (fg)(5) + f(4) can be rewritten as f(5) * g(5) + f(4). This can be solved by evaluating the two functions at 5 and multiplying the two numbers together. Lastly, evaluate the function f at 4 and add it to the previously found product.
In this question:
f(x) = x + 3
g(x) = $x^{2}$ - 2
Evaluate the functions and then multiply:
First we want to evaluate f(x) at x = 5:
f(5) = 5 + 3 = 8
Then we want to evaluate g(x) at x = 5:
g(5) = $(5)^{2}$ - 2 = 25 - 2 = 23
Multiply the numbers together:
(fg)(5) = 8 * 23= 184
Evaluate f(4) and add:
Evaluate f(x) at x = 4:
f(4) = 4 + 3 = 7
Add with the previously found product:
(fg)(5) + f(4) = 184 + 7 = 191
Using both methods (fg)(5) + f(4) = 191
