Home
Class 12
MATHS
If f(x)=ax+b and g(x)=cx+d, then f(g(x))...

If f(x)=ax+b and g(x)=cx+d, then f(g(x))=g(f(x)) is equivalent to

A

f(a) = g(c )

B

f(b) = g(b)

C

f(d) = g(b)

D

f(c ) = g(a)

Text Solution

Verified by Experts

The correct Answer is:
C
f(x) = ax + b
g(x) = cx + d
f(g(x)) = g (f(x))
f(cx + d) = g(ax + b)
a (cx + d) + b = c (ax + b) + d
acx + ad + b = acx + bc + d
ad + b = cb + d
f(d) = g(b)
Promotional Banner

Topper's Solved these Questions

  • SETS, RELATIONS AND FUNCTIONS

    ARIHANT MATHS|Exercise Exercise (More Than One Correct Option Type Questions)|3 Videos

  • SETS, RELATIONS AND FUNCTIONS

    ARIHANT MATHS|Exercise Exercise (Passage Based Questions)|6 Videos

  • SETS, RELATIONS AND FUNCTIONS

    ARIHANT MATHS|Exercise Exercise For Session 3|10 Videos

  • SEQUENCES AND SERIES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|38 Videos

  • THE STRAIGHT LINES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|18 Videos

Similar Questions

Explore conceptually related problems

Let f(x)=px+qandg(x)=mx+n." Then "f(f(x))=g(f(x)) is equivalent to

If f(x)=x^2 and g(x)=x^2+1 then: (f@g)(x)=(g@f)(x)=

If F(x)=f(x)g(x) and f'(x)g'(x)=c , then (F'''(x))/(F(x)) is equal to (where f'(x) denotes differentiation w.rt. x and c is constant) (i) (f')/(f)+(g')/(g) (ii) (f'')/(f)+(g'')/(g) (iii) (f''')/(f)-(g''')/(g) (iv) (f''')/(f)+(g''')/(g)

If f(x)=1+2x and g(x) = x/2 , then: (f@g)(x)-(g@f)(x)=

If f(x)=px+q and g(x)=rx+s and f[g(x)]=g[f(x)]hArr

If f(x)=ax+bandg(x)=cx+d such that f[g(x)]=g[f(x)] then which one of the following is correct?

If f(x)=3x+1 and g(x)=x^(3)+2 then ((f+g)/(f*g))(0) is:

ARIHANT MATHS-SETS, RELATIONS AND FUNCTIONS -Exercise (Single Option Correct Type Questions)
  1. For n,mepsilonN,n|m means that n is a factor of m then relation | is

    Text Solution

    |

  2. The solution of 8x = 6 (mod 14) is

    Text Solution

    |

  3. Let A be a set containing 10 distinct elements,then the total number o...

    Text Solution

    |

  4. Let A and B be two non empty subsets of set X such that A is not a sub...

    Text Solution

    |

  5. f and h are function from A rarr B, where A = {a, b, c, d} and B = {s,...

    Text Solution

    |

  6. Let I be the set of integer and f : I rarr I be defined as f(x) = x^(2...

    Text Solution

    |

  7. Which of the four statements given below is different from other?

    Text Solution

    |

  8. Let A={1,2,..., n} and B={a , b }. Then number of subjections from A i...

    Text Solution

    |

  9. Let f:R to R be defined by f(x)=3x-4. Then, f^(-1)(x) is

    Text Solution

    |

  10. f:R to R is a function defined by f(x)=10x -7, if g=f^(-1) then g(x)=

    Text Solution

    |

  11. Let R be a relation defined by R = {(a, b) : a ge b}, where a and b a...

    Text Solution

    |

  12. If the sets A and B are defined are defined as A={(x,y):y=e^x, x in R}...

    Text Solution

    |

  13. If f : A rarr B is a bijective function, then f^(-1) of is equal to

    Text Solution

    |

  14. If f(y) = (y)/(sqrt(1-y^(2))), g(y) = (y)/(sqrt(1+y^(2))), then (fog) ...

    Text Solution

    |

  15. f:R->R is defined as f(x)=2x+|x| then f(3x)-f(-x)-4x=

    Text Solution

    |

  16. Let R and S be two non-void relations on a set A. Which of the followi...

    Text Solution

    |

  17. Let f:R to R, g: R to R be two functions given by f(x)=2x-3,g(x)=x^(3)...

    Text Solution

    |

  18. If f(x)=ax+b and g(x)=cx+d, then f(g(x))=g(f(x)) is equivalent to

    Text Solution

    |

  19. If f: RvecRvecR are two given functions, then prove that 2m indot{if(x...

    Text Solution

    |

  20. Let f: RvecRa n dg: RvecR be two given functions such that f is inject...

    Text Solution

    |