SOLUTION: Given that a(x)=x^2-5 and b(x)=6x+1 Evaluate (aob)(x) and (boa)(x) I understand that this is (fog)(x) and (gof)(x) So a(b(x)) is how I should insert the functions, but I'm

Algebra ->  Functions -> SOLUTION: Given that a(x)=x^2-5 and b(x)=6x+1 Evaluate (aob)(x) and (boa)(x) I understand that this is (fog)(x) and (gof)(x) So a(b(x)) is how I should insert the functions, but I'm       Log On


   



Question 639388: Given that a(x)=x^2-5 and b(x)=6x+1
Evaluate (aob)(x) and (boa)(x)
I understand that this is (fog)(x) and (gof)(x)
So a(b(x)) is how I should insert the functions, but I'm not sure if I'm doing it right? Please help,
Thank You

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
The idea is to start with the outer function first. Then replace the input with the inner function.

a(x) = x^2-5

a(b(x)) = (b(x))^2-5 ... Replace ALL 'x' terms with b(x)

a(b(x)) = (6x+1)^2-5 ... Replace b(x) on the right side with 6x+1 (since b(x) = 6x+1)

I'll let you expand and simplify this.

-------------------------------------------------------

Now we reverse what we just did

b(x)=6x+1

b(a(x))=6(a(x))+1

b(a(x))=6(x^2-5)+1

I'll let you simplify.