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Given the functions f(x) = 10x + 25 and g(x) = x + 8, which function represents f[g(x)] correctly?


A.) f[g(x)] = 10x + 33

B.) f[g(x)] = 10x2 + 33

C.) f[g(x)] = 10x + 105

D.) f[g(x)] = 10x2 + 105

Verified Answer :

mikearnold1593

It's asking for a composition function where you insert the function g(x) into f(x).
f(g(x))=10(x+8)+25
f(g(x))=10x+80+25
f(g(x))=10x+105

Answer:

Option C is correct

the function f[g(x)] represents correctly is: \(10x+105\)

Step-by-step explanation:

Given the function:

\(f(x) = 10x+25\) and \(g(x) = x+8\)

then;

\(f[g(x)]\)

Substitute the function g(x) we have;

⇒\(f[x+8]\)

Replace x with x+8 in f(x) we have;

⇒\(f[x+8] = 10(x+8)+25\)

Using distributive property: \(a\cdot (b+c) = a\cdot b+ a\cdot c\)

⇒\(f[g(x)] = 10x+80+25 = 10x+105\)

Therefore, the function f[g(x)] represents correctly is: \(10x+105\)

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