Home
Class 12
MATHS
Let f(x)={x^2-4x+3, ,x<3x-4,xgeq3a n dg...

Let `f(x)={x^2-4x+3, ,x<3x-4,xgeq3a n dg(x)={x-3,x<4x^2+2x+2,xgeq4` Describe the function `f/g` and find its domain.

Text Solution

Verified by Experts

The correct Answer is:
`(f(x))/(g(x))={((x^(2)-4x+3)/(x-3)",",x lt 3),((x-4)/(x-3)",",3lt x lt 4),((x-4)/(x^(2)+2x+2)",",x ge 4):} `
`f(x)={(x^(2)-4x+3",",x lt 3),(x-4",",x ge 3):}`
`={(x^(2)-4x+3",",x lt 3),(x-4",",3le x lt 4),(x-4",",x ge 4):} " (1)" `
`g(x)={(x-3",",x lt 4),(x^(2)+2x+2",",x ge 4):}`
`={(x-3",",x lt 3),(x-3",",3 le x lt 4),(x^(2)+2x+2",",x ge 4):} " (2)" `
From (1) and (2), we have
`(f(x))/(g(x))={((x^(2)-4x+3)/(x-3)",",x lt 3),((x-4)/(x-3)",",3lt x lt 4),((x-4)/(x^(2)+2x+2)",",x ge 4):} `
Clearly, `f(x)//g(x)` is not defined at `x=3`. Hence, the domain is `R-{3}.`
Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    CENGAGE|Exercise Exercise 1.4|8 Videos

  • RELATIONS AND FUNCTIONS

    CENGAGE|Exercise Exercise 1.5|5 Videos

  • RELATIONS AND FUNCTIONS

    CENGAGE|Exercise Exercise 1.2|5 Videos

  • Quadratic Equations, Inequalities, Modulus and Logarithms

    CENGAGE|Exercise Question Bank|28 Videos

  • SCALER TRIPLE PRODUCTS

    CENGAGE|Exercise DPP 2.3|11 Videos

Similar Questions

Explore conceptually related problems

Let f(x)=x^2-2x-1 AA x in R Let f:(-oo, a]->[b, oo) , where a is the largest real number for which f(x) is bijective. If f : R->R , g(x) = f(x) + 3x-1 , then the least value of function y = g(|x|) is

Let f(x)={x+1,x >0 2-x ,xlt=0 and g(x)={x+3,x 0)g(f(x)).

Let f(x)={-x^2,for x x^2+8,for x geq 0 the x intercept of the line, that is, the tangent to the graph of f(x) , is zero (b) -1 (c) -2 (d) -4

Let f(x)=|x^2-3x-4|,-1lt=xlt=4 Then f(x) is monotonically increasing in [-1,3/2] f(x) monotonically decreasing in (3/2,4) the maximum value of f(x)i s(25)/4 the minimum value of f(x) is 0

Let y=f(x)=4x^(3)+2x-6 , then the value of int_(0)^(2)f(x)dx+int_(0)^(30)f^(-1)(y)dy is equal to _________.

Let f(x) =4x^2-4ax+a^2-2a+2 be a quadratic polynomial in x,a be any real number. If x-coordinate of vertex of parabola y =f(x) is less than 0 and f(x) has minimum value 3 for x in [0,2] then value of a is

Let P(x) = 4x^(2) - 3x + 2x^(3) + 5 and q(x) = x^(2) + 2x + 4 find p ( x) - q(x) .

Let f(x) = max. {|x^2 - 2| x ||,| x |} then number of points where f(x) is non derivable, is :

Let f(x)=30-2x -x^3 , the number ofthe positive integral values of x which does satisfy f(f(f(x)))) gt f(f(-x)) is