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If
f(x)=x^2-2 and
g(x)=3x, what is
(f\circ g)(2)?

User AnasBakez
by
7.8k points

2 Answers

2 votes

Answer:


\large\boxed{34}

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 :)

User Thepeanut
by
8.1k points
5 votes

Answer:


\boxed{f(6) = 34}

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}.

User Sergey Prokofiev
by
7.6k points

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