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Gr 12 Maths – Functions
Copyright © The Answer
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QUESTIONS and ANSWERS
Work through the Grade 11 Functions downloads first to ensure
your foundation is solid before attempting inverse Functions.
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Gr 12 Maths – Functions: Questions
Copyright © The Answer
2
1. The graph of f is . . .
1.1 If the inverse of f is the reflection of f in the line y =
then the graph of the inverse is:
A. B.
C. D.
(2)
1.2 Consider the graph of f given above.
1.2.1 Write down the equation of the given function and of
the inverse function in the form y = . . . (2)
1.2.2 Hence complete: (a) f (
x
) = . . . (b) f
-1
(
x
) = . . .
1.2.3 Show how the equation of f
-1
could have been
calculated from the equation of f . (2)
1.2.4 Explain why f and f
-1
are both one-to-one
relations. (2)
Sketch the graphs of f and f -1 on the same set of axes,
indicating also the line y =
x
.
3.3 Write down the equation of f
-1
in the form f
-1
(
x
) = . . . .
3.4 Are f and f
-1
both functions? Why (not)?
4. Given: g (
x
) = 3
x
- 2. Determine each of the following:
4.1 g -1 (
x
) 4.2
x g
1
( )
4.3 g
1
x
⎛ ⎞
⎝ ⎠
(6)
5.1 Sketch the graph y = 2
x
, indicating the coordinates of
any three points on the graph. (3)
5.2 Use the three points on the sketch to write down the
coordinates of three points on the inverse function of
y = 2
x
. (3)
5.3 On the same system of axes, sketch the inverse function
of y = 2
x
and the line y = x .
5.4 Describe the transformation from the graph y = 2
x
to its
inverse in words and give the rule for this transformation. (2)
5.5 Write down the equation of the inverse function in the
form
x
= . . .
[In Topic 4, you will convert this equation to y = . . . ] (2)
5.6 Are both the above graphs functions? Why (not)? (2)
5.7 Write down the domain and the range of the graphs of:
(a) y = 2
x
(b)
x
= 2
y
(4)
6. Consider the function f where f (
x
) = 2
6.1 Write down the domain and range of f .
6.2 Sketch the graph of f and g on the same set of axes
where g is the reflection of f in the line y =
x
,
(2)
2. Consider the function f (
x
) = -3
x
+ 6.
2.1 Write down the domain and range of f . (2)
2.2 Determine the equation of the inverse of f in the form
f
-1
(
x
) = . . . (2)
2.3 Sketch the graphs of the functions f , f
-1
and y =
the same set of axes. What do you notice? (3)
x
on
2.4 If f (1) = 3, then f
-1
(3) = . . . ?
2.5 f (2) = 0 ( ; ) lies on f and ( ; ) lies on
3.1 Write down the coordinates of the
x
- and y-intercepts of the
function f (
x
) = 2
x
+ 6 and of f
-1
, the inverse function of f
(1)
f -1 . (2)
. (4)
3.2 Sketch the graphs of f and f -1 on the same set of axes,
indicating also the line y =
x
.
3.3 Write down the equation of f
-1
in the form f
-1
(
x
) = . . . .
3.4 Are f and f
-1
both functions? Why (not)?
4. Given: g (
x
) = 3
x
- 2. Determine each of the following:
4.1 g -1 (
x
) 4.2
x g
1
( )
4.3 g
1
x
⎛ ⎞
⎝ ⎠
(6)
5.1 Sketch the graph y = 2
x
, indicating the coordinates of
any three points on the graph. (3)
5.2 Use the three points on the sketch to write down the
coordinates of three points on the inverse function of
y = 2
x
. (3)
5.3 On the same system of axes, sketch the inverse function
of y = 2
x
and the line y = x .
5.4 Describe the transformation from the graph y = 2
x
to its
inverse in words and give the rule for this transformation. (2)
5.5 Write down the equation of the inverse function in the
form
x
= . . .
[In Topic 4, you will convert this equation to y = . . . ] (2)
5.6 Are both the above graphs functions? Why (not)? (2)
5.7 Write down the domain and the range of the graphs of:
(a) y = 2
x
(b)
x
= 2
y
(4)
6. Consider the function f where f (
x
) = 2
6.1 Write down the domain and range of f .
6.2 Sketch the graph of f and g on the same set of axes
where g is the reflection of f in the line y =
(4)
(2)
(2)
⎜ ⎟
(3)
x
2
(2)
x .