SOLUTION: Please help me solve theses problems: Let f(x)= x^2+2 and g(x)=x+1 a)f(2)= b)g(x)=7 c)f(g(3))= d)g(f(x))= e) f^-1(x)=

Algebra ->  Functions -> SOLUTION: Please help me solve theses problems: Let f(x)= x^2+2 and g(x)=x+1 a)f(2)= b)g(x)=7 c)f(g(3))= d)g(f(x))= e) f^-1(x)=      Log On


   



Question 933421: Please help me solve theses problems: Let f(x)= x^2+2 and g(x)=x+1
a)f(2)=
b)g(x)=7
c)f(g(3))=
d)g(f(x))=
e) f^-1(x)=

Found 2 solutions by Alan3354, MathLover1:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Please help me solve theses problems: Let f(x)= x^2+2 and g(x)=x+1
a)f(2)=
f(x) = x^2+2
Wherever there's an x, replace it with 2
f(2) = 2^2 + 2 = 4+2 = 6
Couldn't be much simpler.
-----
b)g(x)=7
Same as a
==============
c)f(g(3))
Sub 3 for x in g(3), then sub the result in f(x)
---------------
d)g(f(x))
Same as c.
------------------
e) f^-1(x)
This one is different.

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
Let f%28x%29=+x%5E2%2B2 and g%28x%29=x%2B1
a)f%282%29=
f%282%29=+2%5E2%2B2
f%282%29=+4%2B2
f%282%29=+6
b)g%28x%29=7
7=x%2B1
7-1=x
6=x

c)f%28g%283%29%29=
first find g%283%29
g%283%29=3%2B1
g%283%29=4...plug it in for x in f%28x%29
f%284%29=+4%5E2%2B2
f%284%29=16%2B2
f%284%29=18
or
f%28g%283%29%29=%28x%2B1%29%5E2%2B2
f%28g%283%29%29=%283%2B1%29%5E2%2B2
f%28g%283%29%29=4%5E2%2B2
f%28g%283%29%29=16%2B2
f%28g%283%29%29=18

d)g%28f%28x%29%29=
g%28f%28x%29%29=x%5E2%2B2%2B1
g%28f%28x%29%29=x%5E2%2B3

e) f%5E-1%28x%29=
f%28x%29=+x%5E2%2B2....since f%28x%29=+y we have
y=+x%5E2%2B2 ...swap x and y
x=+y%5E2%2B2...solve for y
x-2=+y%5E2
sqrt%28x-2%29=+y
so,f%5E-1%28x%29sqrt%28x-2%29%29