Question

1For f(x) = 7x - 6 and g(x) = 5(x + 6), find (fog)(x) and (gof)(x). Then determine whether (f o g)(x) = (gof)(x).What is (fog)(x)?(fog)(x)=0What is (gof)(x)?(gof)(x) = 0Does (fog)(x) = (gof)(x)?YesооNo

Answer 1

Recall what composition of functions means:

Use one function 's expression as the input of the other function.

so for the case of f(x)=7x=6 and g(x)= 5 (x+6)

we can do the following:

(fog)= f(g(x)) = f (5(x+6)) = 7 (5(x+6)) - 6 = 7 (5x + 30) - 6 = 35 x + 210 - 6 =

35 x + 204.

Now for the second composition:

(gof) = g (f(x))= g (7x-6) = 5 ((7x-6)+6) = 5 ( 7x-6+6) =5 (7x)= 35 x

Therefore these are NOT the same , one gives 35 x + 204, while the other one gives 35 x.

Now for the next question:

If fog (x) = 0 what is the solution for that?

since we found what (fog)(x) is, let's make it equal zero and solve for x:

35 x + 204 = 0

then subtracting 204 from both sides;

35 x = -204

x = -204/35

Now, is (gof)(x) = 0 then we solve for x using the expression we found above:

(gof)(x) = 35 x = 0

that means that x must be zero

x = 0/35 = 0

(fog)(x) is NOT equal to (gof) (x) for the given functions