Let f(x)=3x+1, h(x)=3x2+3x+10. Find g(x) such that f(g(x)) =h(x)

f(g(x))=h(x) 

3g(x)+1=3x2+3x+10

3g(x)=3x2+3x+9

g(x)=x2+x+3

f(x)=6x^2-4x, g(x)=2x, Find (fog)(x)

(fog)(x)=
f(2x)=
6(2x)^2-4(2x)=
24x^2-8x

if f(x)=x^2-15 and g(x)=3-x then (f o g)(x) is? Please help

(f o g)(x)=

f(g(x))=

f(3-x)=

(3-x)^2-15

then you must simplify :)

(fog)(x) for f(x)=2x-3 and g(x)=x^2 - 3x - 2 how do I work this out?

(fog)(x) = 
f(g(x))= 
2g(x)-3= 
2(x^2 - 3x - 2)-3= 
2x^2 - 6x - 7 

:)

Given functions f(x) = 3x and g(x) =x-5, find (f of g)(x)

(f o g)(x)= f(g(x))=f(x-5)=3(x-5) 

:)

Suppose f(x)=2x-8 and g(x)=1x+11 find f(-2) and g(f(-2))

f(-2)=2(-2)-8=4--8=-12 

g(f(-2))=g(-12)= 1(-12)+11=-12+11=-1 



:)

Given f(x)= x^2 + 7 and g(x)= x^2 - 7, find f(g(x))

Solution:

f(g(x)) is a composition - we take a function as an input to another function. 

 

and 

 

g is the input of f so we replace g(x) with the expression - they are equal