Let f(x) = 4x2 + 8x + 7 and g(x) = 3x + 2. Determine the rule for the composite functions f ∘ g and g ∘ f. (g ∘ f)(x) =

(f ∘ g)(x) =

(g ° f)(x) = 12x² + 24x + 23

(f ° g)(x) = 36x² + 72x + 49

Step-by-step explanation:

Here we go. Firstly you have to rewrite f ° g into f(g(x)), that should make it clearer. We, then substitute every x in f by g(x). So:

f(g(x)) = 4(g(x))² + 8(g(x)) + 7

= 4(3x+2)²+8(3x+2)+7

= 4(9x²+12x+4) + 24x + 16 + 17

= 36x² + 48x + 16 + 24x + 16 + 17

finally.. you need to regroup like that:

f ° g(x) = 36x² + 72x + 49

The same thing for g ° f(x)

but this time you substitute by f(x) in g(x) instead.

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)