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8. Let f(x) = 3x and g(x) = (x + 2)^2. Find the value of (g o f)(4).*A.54B.108C.196D.432

User Benibr
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Answer

Option C is correct.

(g o f)(4) = 196

Explanation

f(x) = 3x

g(x) = (x + 2)²

We are then told to find

(g o f)(4)

We need to first interprete what (g o f) means

(g o f) refers to writing g(x) with f(x) replacing x. That is, f(x) replaces all the x that the function given by g(x) has.

(g o f) = g[f(x)]

g(x) = (x + 2)²

g[f(x)] = [f(x) + 2]²

Recall that f(x) = 3x

g[f(x)] = [3x + 2]²

We can then go further now to obtain (g o f)(4)

(g o f)(x) = g[f(x)] = [3x + 2]²

(g o f)(4) = [3(4) + 2]²

= [12 + 2]²

= 14²

= 196

Hence, option C is correct.

(g o f)(4) = 196

Hope this Helps!!!

User Chrisdot
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