MHF4UI
1. Given the graphs of
—I with a domain of {xc9LI—2x6}and g(x)=x,
wfthadominof {xe911—5xX} determine:
Use the gHdnfie right
a) the domain of
(f
—
gx)
b) thegraphof(f-gx).
c) whtethefunction (f—gx).
(Simplify!)
d) write the function [](x). simplify.
(This wiN help you find out wtiat S happening at
the holel)
e) the graph of
2. Given j =
{(— s,g),(— 3,10), (— 2,6),(4,9), (7,12), (io,o)}
a) State the domain of
& g=
b) List the ordered pairs of
f + g.
c) List the ordered pairs of
{(— 3,2), (o,i), (1,5X— 2,—6), (4,—2), (7,—si), (8,—1)},
f + g.
d) List the ordered pairs of
f’ g.
e) Determine g(f(—5)).
f) Determine f(f(—3)).
g) Determinex, if gofx)=1.
h) Determinex, if (gogx)=—6.
÷
3. Given fx) = Sin(i_2rc) and gx) = 3(x
3)2,
evaluate
(f —
4. Given f(x) = 2 in(x 3e) and g(x) = ln(4)+ in(x), evaluate
—
5. Given
(f + g4ej.
f(x)=j!.Ix_41 and g(x)=(x+4, evaluate (f.g—6).
6. Given f(x)=? +1 and g(x)=
fl(5)’
evaluate (f.gin(2)).
7. Given f(x)=3x2 and g(x)=1—x+21, evaluate
8.
Given f(x)=2 and g(x)=asin(.fx)+i evaluate
9. Given f(x)=(6—x)2 and g(x)=log3(x+lo), state the domain of f—g.
10. Given J(x)=
x—2
and g(x)=2x—7,state the domain of f•g.
Sx —20
11. Given f(x)=(x—7)4 and g(x)=x—2, state the domain of f•g.
12. Given g(x) = log3 (6— x) and g(x) = ‘k, state the domain of[L)x).
13. Given f(x)=1—log2(x÷1) and g(x)=6—3x, determine,
a) the domain
d) g(f(7))
of(gofx).
b) the domain of (fogx).
e) x if (gcfx)=2
c) f(g(—1))
x if
(fogx)=_3
14. Determine the equation of the inverse.
a) f(x)=5(x—7)2—12; x7
b) g(x)=54—(x÷6)÷2
c) h(x)=ln(x—9)
15. Use the functions from 14. a), b) and c) to determine the following:
a) f(g(—10))
d) xif(JohXx)=8
(Jogohe15+9)
c)
b) g(J(6))
16. Given the following functions, determine the domain and range of the inverse.
a) y=
x—9
—4
b) f(x)=log(5x—lO)+2
c)
f(x)=22+4X
17. Determine the indicated value for each function.
a) f(x)=22; f’(16)
+4;
2x —3
d) f(x)=.J2x+1—5; f(—2)
c) f(x)=log(Sx—10)+2; f’(4)
— x3, is
18. Given If f(x) = —2x3 and g(x) =
19. Given If f(x) =
N
6
b) f(x)=
odd, even or neither.
y=
and g(x) = 3Sin(x), is y = If. gx) odd, even or neither.
Answers:
1. a)
0
D:{xcI—2x6}
I)
x=6, x=—2
D:
2. a)
c)
c) (f_gx)=1x2_2x
D:{xe911—2x6}
4
h)
If.gx)=x3x2
m) y=2±2gx÷1
{— 3,—2,4,7}.
b)
—1
I—12J5
4.
9. D:{xe9lI—10<x6}
13. a) D:{xe9Ux_i}
14. a)
jx+12
15+21n(4)
g
X
!x2_x
Undefined
k)
f + g = {(— 3,12), (— 2,0), (4,7), (7,2)}
d)
g) x=IO
h)
5.
6.
40
=
{(—
3,5),(— 2_1){4_](7
x=4
5
7.
3
8.
±
4
10. D:{xe7tIx>x4} 11. D:{xe931x7} 12. D:{xc9110<x<6}
b) D:{xeRIx2} c) —1
+7, x—12
b)
15.a) 113
b) 7
16. a) D:{xeR(x—4}, R:{yc9tly9}
c)
j)
[1J(x)=
n) D:{xcmp—1x3},R:{y€91J—2y6}
f g = {(—3,20),(— 2,—36), (4,—I fl(7,—48)}
e)
d)
d) 2.d
x2]26
c) 488
e) x=k—i
c)
o
y=e’+9
d) x=e9+9, x=e5+9
b)
D:{xe9}, R:{ye9y>2}
D:{xe9tJx>0}, R:{ycWI}
j(x)=
17. a) f’(16)=I
b)
18. odd
19. odd
c) f’(4)=18
d) f’(—2)=4