Given the functions a(x) = 3x − 12 and b(x) = x − 9, solve a[b(x)].

a. a[b(x)] = 3x2 – 21
b. a[b(x)] = 3x2 – 39
c. a[b(x)] = 3x – 21
d. a[b(x)] = 3x − 39

option (d) is correct.

a[b(x)] = 3x − 39

Step-by-step explanation:

 Given: a(x) = 3x − 12 and b(x) = x − 9

We have to solve for  a[b(x)]

Function composition is defined as  an operation on two functions such that , where we take function f(x) at x = g(x)

Consider  

Substitute the value of b(x) , we have,

Substitute the value of x as x-9 in a(x) , we have,

Evaluate , we get,

3(x-9) - 12 = 3x - 27 -12 = 3x - 39

Thus, option (d) is correct.

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step-by-step explanation:

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