Question

Find f(g(x)) and g(f(x)) and determine whether the pair of functions f and g are inverses of each other.

f(x)=6x+5 and g(x)= x-5/6
a. f(g(x))= (Simplify your answer.)
b. g(f(x))= (Simplify your answer.)

Answer 1

Explanation:

a. f(x) = 6x+5 and g(x) = x--5/6

f(g(x)) = 6x + 5

Now, let x = g(x) (remember f(x) = 6x+5 so we got the x from f(x))

f(g(x)) = 6(x--5/6) + 5

Open bracket

f(g(x)) = 6(x -- 5/6) + 5

f(g(x)) = x -- 5 + 5

f(g(x) = x

b. g(f(x) = x--5/6

g(f(x) = (6x+5) -- 5/6

g(f(x)) = 6x + 5 -- 5/6

g(f(x)) = 6x/6

g(f(x)) = x...

To check for inverse

1/g(f(x) = 1/x

1/f(g(x) = 1/x

Meaning 1/f(g(x) = 1/g(f(x) inverse of each other

#AllonGod