Question

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

Answer 1

a(x) = 3x - 12
b(x) = x - 9

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

Answer 2

option (d) is correct.

a[b(x)] = 3x − 39

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
`P(x)=f(g(x))` , where we take function f(x) at x = g(x)

Consider
`a[b(x)]=a(b(x))`

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

`a(b(x))=a(x-9)`

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

`a(x-9)=3(x-9)-12`

Evaluate , we get,

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

Thus, option (d) is correct.