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Mathematics
Problem
Let
f
:
R
→
R
f:\mathbb R\to\mathbb R
f
:
R
→
R
be defined by
f
(
x
)
=
3
x
−
4
f(x)=3x-4
f
(
x
)
=
3
x
−
4
. Denote its inverse by
f
−
1
f^{-1}
f
−
1
. (i) Find
f
−
1
(
x
)
f^{-1}(x)
f
−
1
(
x
)
. (ii) Without expanding unnecessary intermediate results, evaluate
f
−
1
(
f
(
f
−
1
(
7
)
)
)
f^{-1}\bigl(f\bigl(f^{-1}(7)\bigr)\bigr)
f
−
1
(
f
(
f
−
1
(
7
)
)
)
and justify each step used in the simplification.
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