SOLUTION: Please help me with this question. Thank you! a) Given the functions f(x) = x + 2 and g(x) = 3^x, determine an equation for (f ∘ g)(x) and (g ∘ f)(x). b) Determine f(g(3)) an

Algebra ->  Test -> SOLUTION: Please help me with this question. Thank you! a) Given the functions f(x) = x + 2 and g(x) = 3^x, determine an equation for (f ∘ g)(x) and (g ∘ f)(x). b) Determine f(g(3)) an      Log On


   

Question 1162538: Please help me with this question. Thank you!
a) Given the functions f(x) = x + 2 and g(x) = 3^x, determine an equation for (f ∘ g)(x) and (g ∘ f)(x).
b) Determine f(g(3)) and g(f(3)).
c) Determine all values of x for which f(g(x)) = g(f(x)).
Found 2 solutions by solver91311, MathLover1:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


a)



Follow the same procedure to find

b) Write the two expressions in pencil. Erase every instance of and write in place of every . Do the arithmetic.

c) Set



and solve for x.















John

My calculator said it, I believe it, that settles it

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29+=+x+%2B+2+and
g%28x%29+=+3%5Ex
determine an equation for:
a.
(f ∘ g)(x) =f%28g%28x%29%29=f%283%5Ex%29=3%5Ex%2B2
and
(g+∘ f)(x)=g%28f%28x%29%29=g%28x%2B2%29=3%5E%28x%2B2%29
b. Determine f%28g%283%29%29 and g%28f%283%29%29.
first g%283%29+=+3%5E3=27
f%28g%283%29%29=x%2B2=27%2B2=29

f%283%29+=+x+%2B+2=3%2B2=5+
g%28f%283%29%29=3%5Ex=3%5E5=243



c) Determine all values of x for which f%28g%28x%29%29+=+g%28f%28x%29%29.
x%2B2=3%5Ex....evidently, one solution is x=1
verify:

1%2B2=3%5E1
3=3->true