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Mathematics
Mathematics
Problem
Let
f
:
R
→
R
f: \mathbb R \to \mathbb R
f
:
R
→
R
be given by
f
(
x
)
=
3
x
−
7
f(x)=3x-7
f
(
x
)
=
3
x
−
7
. a. (i) Find
f
−
1
(
x
)
f^{-1}(x)
f
−
1
(
x
)
. b. (ii) State the domains and the ranges of
f
f
f
and
f
−
1
f^{-1}
f
−
1
. c. (iii) Verify that
f
(
f
−
1
(
x
)
)
=
x
f\bigl(f^{-1}(x)\bigr)=x
f
(
f
−
1
(
x
)
)
=
x
and
f
−
1
(
f
(
x
)
)
=
x
f^{-1}\bigl(f(x)\bigr)=x
f
−
1
(
f
(
x
)
)
=
x
for all admissible
x
x
x
. Write the set of admissible values expressly in each case.
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