Answer:
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 [tex]P(x)=f(g(x))[/tex] , where we take function f(x) at x = g(x)
Consider [tex]a[b(x)]=a(b(x))[/tex]
Substitute the value of b(x) , we have,
[tex]a(b(x))=a(x-9)[/tex]
Substitute the value of x as x-9 in a(x) , we have,
[tex]a(x-9)=3(x-9)-12[/tex]
Evaluate , we get,
3(x-9) - 12 = 3x - 27 -12 = 3x - 39
Thus, option (d) is correct.
