Composing & Inverting Functions — Drills
Composing & Inverting Functions has 7 drill skills. Each one generates fresh questions every time, with a hint and full worked steps, so you can keep practising a single skill until it settles.
What these drills cover
These questions use 3 ideas from the course. Follow any of them for a definition, where it is taught, and what it leads to.
- Function — A rule pairing each input with exactly one output.
- One-to-one — No two inputs share an output. Only a one-to-one function has an inverse that is itself a function.
- Horizontal line test — If any horizontal line meets a graph twice, the function is not one-to-one.
Adding
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
For f(x)=3x+7 and g(x)=4x-2, find (f+g)(3).
Worked answer
26
f(3)=3(3)+7=16
g(3)=4(3)-2=10
16+(10)=26
Problem 2
For f(x)=4x+6 and g(x)=2x-9, find (f+g)(5).
Worked answer
27
f(5)=4(5)+6=26
g(5)=2(5)-9=1
26+(1)=27
Mult
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
For f(x)=x+8 and g(x)=x-6, find (fg)(3).
Worked answer
-33
f(3)=11
g(3)=-3
11 × -3 = -33
Problem 2
For f(x)=x+1 and g(x)=x-5, find (fg)(5).
Worked answer
0
f(5)=6
g(5)=0
6 × 0 = 0
Composing functions
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
For f(x)=x+3 and g(x)=5x+6, find f(g(6)).
Worked answer
39
g(6)=5(6)+6=36
f(36)=36+3=39
Problem 2
For f(x)=x+7 and g(x)=2x+5, find f(g(5)).
Worked answer
22
g(5)=2(5)+5=15
f(15)=15+7=22
Ordering
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
For f(x)=x+6 and g(x)=4x, find g(f(6)).
Worked answer
48
f(6)=12
g(12)=4 × 12 = 48
Note f(g(6))=30 — different
Problem 2
For f(x)=x+5 and g(x)=5x, find g(f(3)).
Worked answer
40
f(3)=8
g(8)=5 × 8 = 40
Note f(g(3))=20 — different
Formula
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
For f(x)=6x-2 and g(x)=x+5, write (f ° g)(x) in the form mx+n.
Worked answer
6x+28
6(x+5)-2
=6x+30-2
=6x+28
Problem 2
For f(x)=2x-5 and g(x)=x+4, write (f ° g)(x) in the form mx+n.
Worked answer
2x+3
2(x+4)-5
=2x+8-5
=2x+3
Inverses
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Find f-1(x) for f(x)=5x + 6. Give it as a single fraction.
Worked answer
(x-6)/5
x=5y + 6
x - 6 = 5y
y=x - 65
Problem 2
Find f-1(x) for f(x)=2x - 5. Give it as a single fraction.
Worked answer
(x+5)/2
x=2y - 5
x + 5 = 2y
y=x + 52
Verify
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
If f(x)=2x-6, find f-1(6).
Worked answer
6
2x-6=6
2x=12
x=6
Problem 2
If f(x)=4x-5, find f-1(3).
Worked answer
2
4x-5=3
4x=8
x=2