If f(x)=x2−1,g(x)=2x+5, then find (fog)(x).
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Answer:
Another way of looking at it:
set
g
(
x
)
→
y
1
=
x
+
2
...
...
...
.
.
E
q
u
a
t
i
o
n
(
1
)
set
f
(
x
)
→
y
2
=
2
x
−
5
...
...
.
.
E
q
u
a
t
i
o
n
(
2
)
(
f
o
g
)
(
x
)
is such that as f is before the g in
(
f
o
g
)
(
x
)
so wherever in
f
(
x
)
you see
x
you substitute
y
1
That is; you are substituting
E
q
u
a
t
i
o
n
(
1
)
into any
x
that is in
E
q
u
a
t
i
o
n
(
2
)
So:
(
f
o
g
)
(
x
)
=
2
(
y
1
)
−
5
but
y
1
=
x
+
2
So:
(
f
o
g
)
(
x
)
=
2
(
x
+
2
)
−
5
(
f
o
g
)
(
x
)
=
2
x
+
4
−
5
=
2
x
−
1
Hope it helps you
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