let F:R-R. be defined by f(x)=x*2+2x.
find fof(2)?
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Answer:
ANSWER
f:R→R
f(x)=x
2
+2
g:R→R
g(x)=
x−1
x
fog(x)=f(g(x))
=f(
x−1
x
)
=(
x−1
x
)
2
+2
=
x
2
−2x+1
x
2
+2
=
x
2
−2x+1
x
2
+2(x
2
−2x+1)
=
x
2
−2x+1
x
2
+2x
2
−4x+2
=
x
2
−2x+1
3x
2
−4x+2
fog(2)=
2
2
−2×2+1
3×2
2
−4×2+2
=
4−4+1
3×4−8+2
=
1
12−6
=6
gof(x)=g(f(x))
=g(x
2
+2)
=
x
2
+2−1
x
2
+2
=
x
2
+1
x
2
+2
gof(−3)=
(−3)
2
+1
(−3)
2
+2
=
9+1
9+2
=
10
11
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