Given that f(x) = 5x − 10 and g(x) = x + 3, Solve for f(g(x)) when x = −1.

We will use the concept of functions to solve the given problem.

Answer: If f(x) = 5x − 10 and g(x) = x + 3, then the value of f(g(-1)) is 0.

Let us solve it step by step.

Explanation:

Given:

f(x) = 5x − 10 ------------- (1)

g(x) = x + 3 ------------ (2)

Both f(x) and g(x) are functions of x and dependent on the value of x. 

We have to find composite function f(g(x)).

⇒ f(g(x)) = 5{g(x)} - 10

Using (1) and (2) we have,

⇒ f(g(x)) = 5(x + 3) - 10

⇒ f(g(x)) = 5x + 5

Now let us solve this for x = -1.

⇒ f(g(-1)) = 5(-1) + 5

⇒ f(g(-1)) = -5 + 5

⇒ f(g(-1)) = 0

Thus, if f(x) = 5x − 10 and g(x) = x + 3, then f(g(-1)) is 0.