Exercise 1 - Weebly



Important Questions for SLC Examination

Short Answer Questions

1. If f(x) = x+2 , g(x) = x -4 and h(x) = 3x, find the following:

a. fog(x)

b. goh(x)

c. hof(x)

2. If f(x) = 3x+4 find the following functions.

a. f-1(x)

b. f-1(4)

c. f(2) .f-1(2)

d. f(2) [pic] f-1(2)

3. If f and g are the functions defined by f = {(1, 5), (2, 4) , (3, 6)} and g {(5, 3), (4, 1), (6, 2)} Find the composite function gof and fog

4. If f(x) = 3x + 2 and g(x) = 2x – 1, find gof(x).

5. If f(x) = 14x + 12 and g(x) = 5x – 21, find fog(x).

6. If f(x) = x + 12 and g(x) = 2x + 12, find fog(x).

7. If f(x) = 3x - 2 and g-1(x) = 2x +1, find gof(x) and fog(x).

8. If f(x) = 3x + 12 and g-1(x) = x -10, find gof(x) and fog(x).

9. If f and g are the functions defined by f = {(1, 2), (3, 5) , (4, 1)} and g {(2, 3), (5, 1), (1, 3)} Find the composite function gof and fog

10. If f: x (3x +1 and h: x(4x, Find the equation of foh(x) and hof(x) and value of hof (2), foh (2) and ff (-5).

11. If f: R ( R is defined by f(x) = 2x and g: R ( R is defined by f(x) = x + 1. Find gof and fog.

12. If f : {(x, 3x)} and g : {x, 2x + 5} find fog-1 (x) and gf-1(x)

13. If f(x) = x2 and g(x) = x- 3 Find (i) fog(x) (ii) gof(x) (iii) fog(5) (iv) gof(3)

14. If f(x) = 2x2 and g(x) = 5x+ 3 Find (i) fog(x) (ii) gof(x) (iii) fog(4) (iv) gof(-1)

15. Find the inverse of the following functionf

a. [pic]

b. [pic]

c. [pic]

d. [pic]

16. If f(x) = 2x + 4 is function. Find f1 and draw the graphs of both the functions.

17. If f-1(x) = 2x - 1 is function. Find f(x) and draw the graphs of both the functions.

Long Answer Questions

1. If f(x) = x2 – 2x, g(x) = 2x + 3 and fog-1(x) = 3 then find the value of x.

2. If f(x) = [pic] and g(x) = 2 +a, evaluate fog(x) = g-1(x) to find the value of a.

3. Let A = {-1, 0, 1} and B = {0, 1}.The function f: A→B is defined by f(x) = x2. Can f-1(x) be defined?

4. It is given that f(x) = 4x – 17 and[pic]. If f(x) = g-1(x), find the value of x

5. It is given that f(x) = 5x – 9 and[pic]. If f(x) = g-1(x), find the value of x

6. It is given that f(x) = 3x – 7 and[pic]. If f-1(x) = g(x), find the value of x

7. It is given that f(x) = 4x –5 and[pic]. If f(x) = g-1(x), find the value of x

8. It is given that f(x) = 9x +15 and[pic]. If f-1(x) = g-1(x), find the value of x

9. If f(x) = 1 + 2x and g(x) =, find g-1 and fog (-1). is fog(x) = gof(x)?

10. If f(x) = 10 -3x and g(x) =, find g-1 and fog (5). is f-1og(x) = gof-1(x)?

11. If f(x) = 3x + a and fof (6) = 10 find the value of a and f-1 (4).

12. If f(x) = 5x - k and fof (-3) = 1 find the value of k and f-1 (-5).

13. Find the inverse function of the following functions and show that fof-1 is an identity.

a. f(x) = 3x – 1

b. f(x) = 5x + 7

c. g(x) = 8x - 17

d. p(x) = x + 9

14. If f = {(x, 3x - 4): x X R}, XR}, g = {(x, -2x + 1): x XR} and h = {(x, x+3): x XR} are functions. Prove that fof1, gog-1, h-1oh are identity function.

15. Given that f(x) = 2x + 3 and fog(x) = 6x + 13, find g(x)

16. Given that g(x) = 3x + 5 and fog(x) = 6x + 13, find f(x)

17. Given that g(x) = 3x - 5 and fog(x) = 4x + 3, find f(x)

18. Given that f(x) = 2x + 3, g(x) = 3x + 5 and gohof(x) = 6x + 17, find h(x).

................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download