Final answer:
The value of (f(g(-3))) is 35, which is found by first calculating g(-3) and then applying that value to the function f(x).
Step-by-step explanation:
For example, if we let f be the function given by f(x) = x2 and let g be the function given by g(x) = x + 3, then the composition of g with f is called gf and is worked out as gf(x) = g(f(x)) . gf(x) = g(f(x)) = g(x2) = x2 + 3 .
A function whose values are found from two given functions by applying one function to an independent variable and then applying the second function to the result and whose domain consists of those values of the independent variable for which the result yielded by the first function lies in the domain of the second.
To find (f(g(-3)), we first need to evaluate g(-3). Using the function g(x) = -2x + 1, we substitute -3 for x:
g(-3) = -2(-3) + 1 = 6 + 1 = 7.
Now, we apply the value of g(-3) to the function f(x) which is defined as f(x) = 5x:
f(g(-3)) = f(7) = 5(7) = 35.