Use f(x) = 5x − 2 and g(x) = 3 − x2 to evaluate the expression.

Question

(a)   (f ∘ g)(−2)

(b) (g ∘ f)(−2)

Use f(x) = 4x − 2 and g(x) = 3 − x^2 to evaluate the expression

(a) (f ∘ g)(x)

(b) (g ∘ f)(x)

Answer 1

Hi,

Use f(x) = 5x − 2 and g(x) = 3 − x2 to evaluate the expression.

(a)   (f ∘ g)(−2)

(b) (g ∘ f)(−2)

You need to know the meaning of fog that it will be :

fog = f ( 9 (x) ) by another word, replace g(x) instead of x in function f(x)

f(g(x)) = 5 (g(x)) -2 = 5( 3-x^2) - 2 = 15 - 5x^2 -2 = 13 - 5x^2

now you can find fog for any point such as -2

(f ∘ g)(−2) = 13 - 5 (-2)^2 = 13- 20 = -7

gof is the same meaning only replace f(x) instead of x in g(x)= 3 - x^2

gof = g( f(x) )= 3 − (f(x))2 = 3 - (5x -2 )^2

Now you can find gof for any given x.

I hope it is useful,

Minoo

Answer 2

a) fog=f(g(-2)) , g(-2)=3-4= -1 , f(-1)=-5-2=-7

b)gof(-2)= g(f(-2)), f(-2)=5(-2)-2= -10-2=-12 , g(-12)=3-144=-141