Question

If f (x) = 3x + 1 and g(x) = 2x + 1, what is the value of f (g(2))? 13 14 15 16

Answer 1

To find the value of f(g(2)), we need to substitute the value of 2 into g(x) and then substitute the result into f(x).

First, let's find the value of g(2):

g(x) = 2x + 1

g(2) = 2(2) + 1

g(2) = 4 + 1

g(2) = 5

Now that we know g(2) = 5, let's substitute this value into f(x):

f(x) = 3x + 1

f(g(2)) = f(5)

f(g(2)) = 3(5) + 1

f(g(2)) = 15 + 1

f(g(2)) = 16

Therefore, the value of f(g(2)) is 16.

Answer 2

f(g(2)) = 16

Explanation:

The expression f(g(2)) represents a composite function.

To evaluate the composite function, first find the value of the inner function g(2) by substituting x = 2 into function g(x). Then substitute the result as the input for the outer function f(x).

Substitute x = 2 into g(x) to find g(2);

`\begin{aligned}g(2)&=2(2)+1\\&=4+1\\&=5\end{aligned}`

Now, substitute the result of g(2) as the x-value of function f(x):

`\begin{aligned}f(5)&=3(5)+1\\&=15+1\\&=16\end{aligned}`

Therefore, f(g(2)) = 16.