Question

f(x) = 7x + 7, g(x) = 6x2

Find (fg)(x).

6x2 + 7x + 7

42x3 + 42x2

42x2 + 42x

42x + 42

Answer 1

Hint:

(fg)(x)

is the same as

f(x) * g(x)

Answer 2

@jim_thompson5910 well then i know the answer is 42x3 + 42x2

Answer 3

you are correct

Answer 4

could you also help we with
Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x.
f(x)= x^2-3 and g(x)= sqrt 3+x
I have a hard time explaining

Answer 5

@jim_thompson5910

Answer 6

f(x) = x^2 - 3

f(g(x)) = (g(x))^2 - 3

f(g(x)) = ( sqrt(3+x) )^2 - 3

f(g(x)) = 3+x - 3

f(g(x)) = x

Do the same thing (but in reverse order) to find g(f(x))

Answer 7

g(x)= sqrt 3+x
The bigger problem was the sqrt portion Im not even sure help? @jim_thompson5910

Answer 8

g(x) = sqrt(3+x)

g(f(x)) = sqrt(3+f(x))

g(f(x)) = sqrt(3+x^2 - 3)

....

keep going

Answer 9

THen sqrt x^2
then x
?
@jim_thompson5910

Answer 10

yes, you got it