Question

Please show me how to solve this?
F(x) = 1/x-5 and g(x) = x^2+2
Find:
A... (f o g)(x)
B... (g o f)(6)

Answer 1

to get (fog)(x) just replace x in f(x) by g(x)

Answer 2

You're going to replace the x in f(x) with g(x), so it'll be f(g(x)) = 1/(x^2+2)-5.

Answer 3

So the answer would be 1/-3... ?

Answer 4

where did u get 1/-3 from ?

Answer 5

1 all over (x^2+2)-5
x^2+2 = 2 - 5 = -3

Answer 6

why x^2+2 = 2 - 5 = -3 ??
(fog) (x) is just 1 all over( (x^2+2)-5)
ok ?

Answer 7

I don't solve it any further?

Answer 8

then u get 1 all over( (x^2+2)-5) = 1 all over(x^2-3)

Answer 9

Ohhhh. Ok, that makes sense.

Answer 10

now find (gof)(x)

Answer 11

Do I take 1 all over x^2-3 and replace the x with 6?
Or do I start with the original equations?

Answer 12

to find (gof)(x) replace all 'x' in g(x) by f(x) = 1/(x-5)

Answer 13

so start with original equations

Answer 14

Sooo.
g(6) = 1 all over 6-5 = 1 then g(1) = 1^2+2 = 3

Answer 15

that is correct, u just made one typo:
f(6) = 1 all over 6-5 = 1 then g(1) = 1^2+2 = 3

Answer 16

so (gof)(6)=3

Answer 17

Thaaaaank you so much!

Answer 18

welcome :)