Given that f(x) = 2x + 1 and g(x) = −5x + 2, Solve for f(g(x)) when x = 3.

We will first find the value of f(g(x)), and then solve it for x = 3.

Answer: If f(x) = 2x + 1 and g(x) = −5x + 2, then f(g(3)) = -25.

Let us solve it step by step.

Explanation:

Given that, f(x) = 2x + 1 and g(x) = −5x + 2.

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

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

f(g(x)) = 2{g(x)} + 1

f(g(x)) = 2(-5x + 2) + 1

f(g(x)) = -10x + 4 + 1

f(g(x)) = -10x + 5

Now let us solve this for x = 3,

f(g(3)) = -10(3) + 5

f(g(3)) = -30 + 5

f(g(3)) = -25

Thus, if f(x) = 2x + 1 and g(x) = −5x + 2, then f(g(3)) = -25.