Composite And Inverse

Malang Study Club

1. Given f : R 6 R define by x2 – 2x + 1. a. Determine f(2), f(0), f(a), f(b2), f(2a + b), f(x + 5)! b. If f(p) = 16, find p! c. Determine the range of f, if the domain given as below : i.

Df = {x : -1 ≤ x < 2, x Є R}

iii. Df = {x : -1 < x < 3, x Є R}

ii. Df = {x : -2 ≤ x ≤ 3, x Є R}

iv. Df = {x : x Є R}

x −1

2. Given f : R 6 R define by

x

x − 1 . Determine the domain 2

and g : R 6 R define by

and range for : a. f

d. f – g

b. g

e.

c. f + g 3. Given

{(4,7),(1,2),(0,-1),(-1,3)}

f :R 6 R

f g

and

g : R 6 R {(2,1),(3,4),(6,-1),(7,0)}.

Determine : a. gf b. fg c. domain and range of gf and fg 4. Given f : R 6 R

x+4 x −6

and g : R 6 R(2 x − 1) . Calculate :

a. fg

c. f2

e. f-1

g. (fg)-1

i.

f(1)

k. f-1(0)

b. gf

d. g2

f.

g-1

h. (gf)-1

j.

g2(1)

l.

(gf)-1(0)

5. Find f! a. f-1 =

2x

x −6 2

b. f-1 =

3−x

5

6. Find the other function! a.

g : R 6 R(2 x + 1) and gf = 6 x + 4 x − 7 2

⎛1− x ⎞ b. f : R 6 R ⎜ ⎟ and fg = 7 x ⎝ 2x ⎠

(

)

c.

g : R 6 R 10 x − 3 and fg = 30 x − 15

d.

f : R 6 R⎜

7. If f =

2

g : R 6 R( x + 3) and ( gf ) =

f.

f : R 6 R( x − 3) and ( gf ) =

−1

2

x+3 2 1 2

x +1

x −5 ⎛ x −5⎞ ⎟ and gf = x −1 ⎝ x ⎠

2

x + 1 and fg =

8. Given f = 2x – 3, g = 9. If g = 2x + 1 and gf =

10. If f =

−1

e.

4x − 1 2 − 3x

1

2

x−2

x − 4 x + 5 , determine g(x-3)!

x + 2 , and h = x3 + x2. Calculate hgf(1)! 2x − 3 x+2

, determine f-1(1)!

is inverse of g, find fg(1)!

11. If g = x2 – 4x + 6 and gf = 4x2 – 4x + 3, and f(2) = -1. Find f! 12. Given f = x – a, g = 3x + b. gf(0) = 1, fg (1) = (gf)-1 (1). Calculate f-1 (1) + g(1)!

Latihan Matematika SMA XI IPA

Composite and Inverse

Malang Study Club

13. Find a! a. f = x2 – 2, g = sin x, and fg (a) = −

7 4

, 0 ≤ a ≤ 2π

b. f = 3 + 2x, g = 2 + x, h = 2x, and (fgh)-1 (a) = -1 c. f = 2x2 + 3x + a and f-1 (1) = 3 d. f = x2, g = 1 – 2x, and fg(a) = 25 14. If f = 52x, calculate f-1(25)! 15. Given f =

5x + 3 2x − 1

,x ≠

1 2

and g = 3 x + 2 . Determine f-1g!

Latihan Matematika SMA XI IPA

Composite and Inverse