SME
Grade 11 Math · Problem type
Add, subtract, multiply and divide functions
Use this for “f(x) = 2x − 1 and g(x) = x + 4. Find (f + g)(3), (f − g)(3), (f · g)(3) and (f ÷ g)(3).”
Chart
f(3) = 5
Sum, (f + g)(x): 12
Difference, (f − g)(x): −2
Product, (f · g)(x): 35
Quotient, (f ÷ g)(x): 5/7
This is an example. Type your own values to start a new problem.
f(x)
=
a
x
+
(
b
)
g(x)
=
c
x
+
d
(f
+
g)(
)
=
S
F
Value of f, f(x)
worked out (not typed)
G
Value of g, g(x)
worked out (not typed)
D
Difference, (f − g)(x)
worked out (not typed)
P
Product, (f · g)(x)
worked out (not typed)
Q
Quotient, (f ÷ g)(x)
worked out (not typed)
Formulas
F
=
a
×
x
+
b
5 = 2 × 3 + (−1)
G
=
c
×
x
+
d
7 = 1 × 3 + 4
S
=
F
+
G
12 = 5 + 7
D
=
F
−
G
−2 = 5 − 7
P
=
F
×
G
35 = 5 × 7
Q
=
F
G
5
7
=
5
7
Assumptions
•
(f + g)(x) = f(x) + g(x): find each function’s value at x, then add.
•
Subtract, multiply or divide the same way: (f − g)(x) = f(x) − g(x), and so on.
•
f ÷ g has no value where g(x) = 0: those x are left out of its domain.
Step-by-step
WE KNOW
a = 2, b = −1, c = 1, d = 4, x = 3
FIND
value of f, f(x) (F), value of g, g(x) (G), sum, (f + g)(x) (S), difference, (f − g)(x) (D), product, (f · g)(x) (P), quotient, (f ÷ g)(x) (Q)
Step 1 · Find value of f, f(x): F
Use F = a × x + b
Put
x
into
f.
F
=
2
×
3
−
1
F
=
6
−
1
F
=
5
Step 2 · Find value of g, g(x): G
Use G = c × x + d
Put
x
into
g.
G
=
1
×
3
+
4
G
=
7
Step 3 · Find sum, (f + g)(x): S
Use S = F + G
Add
the
two
values
at
x
.
S
=
5
+
7
S
=
12
Step 4 · Find difference, (f − g)(x): D
Use D = F − G
Take g’s value from f’s.
D
=
5
−
7
D
=
−2
Step 5 · Find product, (f · g)(x): P
Use P = F × G
Multiply
the
two
values
at
x
.
P
=
5
×
7
P
=
35
Step 6 · Find quotient, (f ÷ g)(x): Q
Use Q = F ÷ G
Divide f’s value by g’s.
Q
=
5
7
Q
=
5
7
Check
Put the numbers back in. Both sides should match.
5 = 2 × 3 − 1 ✓
7 = 1 × 3 + 4 ✓
12 = 5 + 7 ✓
−2 = 5 − 7 ✓
35 = 5 × 7 ✓
5
7
=
5
7
✓
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