What is the value of fg(x) when x equals 1, given that f(x) is defined as 5x + 10 and g(x) is defined as x + 3?

To determine the value of fg(x) when x equals 1, we need to evaluate the composite function fg(x). This means we will first find g(1) and then use that result to find f(g(1)).

Step 1: Calculate g(1)

The function g(x) is defined as:

g(x) = x + 3

Substituting x = 1 into g(x):

g(1) = 1 + 3 = 4

So, g(1) equals 4.

Step 2: Calculate f(g(1)) or f(4)

The function f(x) is defined as:

f(x) = 5x + 10

Now, we will substitute x = 4 into f(x):

f(4) = 5(4) + 10 = 20 + 10 = 30

Thus, f(g(1)) or fg(1) equals 30.

Final Answer

In conclusion, the value of fg(1) is 30.