Question

If class="latex-formula"> and $g(x)=3x$, what is $(f\circ g)(2)$?

Answer 1

Answer:

$\large\boxed{34}$

Step-by-step explanation:

$f(x) = x^2 - 2$

$g(x) = 3x$

$(fog)(2)$

Find g(2)

$g(x) = g(2)$

$x=2$

$3x = 3(2) = 6$

$g(2) = 6$

Find f(6)

$f(x) = x^2-2$

Substitute

$f(6) = x^2 - 2$

$x^2 - 2 = 6^2 - 2$

$36 - 2 = 34$

$\large\boxed{34}$

Hope this helps :)

Answer 2

Answer:

$\boxed{f(6) = 34}$

Step-by-step explanation:

Composition of functions occurs when we have two functions normally written similar or exactly like f(x) & g(x) - you can have any coefficients to the (x), but the most commonly seen are f(x) and g(x). They are written as either f(g(x)) or (f o g)(x). Because our composition is written as $(f \circ g)(2)$, we are replacing the x values in the g(x) function with 2 and simplifying the expression.

$g(2) = 3(2)$

$g(2) = 6$

Now, because we are composing the functions, this value we have solved for now replaces the x-values in the f(x) function. So, f(x) becomes f(6), and we use the same manner as above to simplify.

$f(6) = (6)^2-2$

$f(6) = 36-2$

$f(6) = 34$

Therefore, when we compose the functions, our final answer is $\bold{f(6) = 34}$.