# 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 fog(x)
2. If f(x) = 3x+4 find the following functions.
a. f1(x)
c. f(2) .f-1(2)
b. f-1(4)
d. f(2)  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. f ( x) 
3x  1
; x  2
x2
c.
f ( x) 
5x  3
1
;x  
3x  1
3
b. f ( x) 
4x  5
1
;x 
2x 1
2
d.
f ( x) 
5x  4
5
;x 
3x  5
3
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) =
x2
and g(x) = 2 +a, evaluate fog(x) = g-1(x) to find the value of a.
x2
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?
2x  8
. If f(x) = g-1(x), find the value of x
5
7x  8
It is given that f(x) = 5x – 9 and g ( x) 
. If f(x) = g-1(x), find the value of x
3
4x  2
It is given that f(x) = 3x – 7 and g ( x) 
. If f-1(x) = g(x), find the value of x
3
3x  1
It is given that f(x) = 4x –5 and g ( x) 
. If f(x) = g-1(x), find the value of x
2
7 x  11
It is given that f(x) = 9x +15 and g ( x) 
. If f-1(x) = g-1(x), find the value of x
21
1
1
If f(x) = 1 + 2x and g(x) =
, find g-1  and fog (-1). Is fog(x) = gof(x)?
1-x
2
4. It is given that f(x) = 4x – 17 and g ( x) 
5.
6.
7.
8.
9.
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1
1
, find g-1  and fog (5). Is f-1og(x) = gof-1(x)?
1-x
2
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
c. g(x) = 8x - 17
10. If f(x) = 10 -3x and g(x) =
b. f(x) = 5x + 7
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 fof 1, gog1, 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).
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