Precalculus Skill Builders Vol 1 Solutions

10. Inverses
Example: Find the inverse of f (x) = x!2
x
Solution: y = x!2
x
Start by replacing f(x) with y.
x = y!2
2
xy = y ! 2 Solve for y.
xy ! y = 2
y(x ! 1) = 2
y = 2
x!1
Interchange x and y in the equation.
f 1 (x) = 2
x!1 Replace y with f !1 (x) .
Find the equation of the inverse for each function below.
1. f (x) = 3x + 1
[ f !1 (x) = x!1
3
]
3. f (x) = x 2 + 5
[ f !1 (x) = ± x ! 5 ]
5. f (x) = x!4
5
[ f !1 (x) = 5x + 4 ]
7. f (x) = 3 4 x + 8
[ f !1 (x) = 4 3 (x ! 8) ]
9. f (x) = 3 x
[ f -1 (x) = log 3 x ]
2. f (x) = 5 ! 6x
[ f !1 (x) = 5– x
6
]
4. f (x) = 4x 2
[ f !1 (x) = ± x
2
]
6. f (x) = x+10
11
[ f !1 (x) = 11x ! 10 ]
8. f (x) = 7 ! x 2
[ f !1 (x) = 7 – x ]
10. f(x) = log x
[ f -1 (x) = 10 x ]
11. f (x) = x+3
12. f (x) = x!4
x
x
[ f !1 (x) = x!1 3 ] [ f !1 (x) = 4
13. f (x) = 11x!12x2
x
[ f !1 (x) = 11– x
12
]
1! x ]
14. f (x) = 3x+4
5x
[ f !1 (x) = 4
5x! 3 ]
15. f (x) = 10x!15x2
16. f (x) = 7x!4
5x 2
3x
[ f !1 (x) = x+ 2 ] [ f !1 (x) = !4
3
3x –7 ]
Pre-Calculus with Trigonometry