Home
Class 12
MATHS
Represent the following function:f: f(x^...

Represent the following function:`f: f(x^2+x+3)+2f(x^2−3x+5)=6x^2 −10x+17` in the form of ax + b.

Text Solution

Verified by Experts

The correct Answer is:
`f(x)=2x-3`
Obviously, `f` is a linear polynomial.
Let `f(x)=ax+b.` Hence,
`f(x^(2)+x+3)+2f(x^(2)-3x+5)=6x^(2)-10x+17`
or ` [a(x^(2)+x+3)+b]+2[a(x^(2)-3x+5)+b]=6x^(2)-10x+17`
or `a+2a=6 " (1) " `
and `a-6a= -10 " (2)" `
or `a=2 " " ` (Comparing coeff. of `x^(2)` and coeff. of `x` both sides)
Again, `3a+b+10a+2b=17`
or `6+b+20+2b=17`
` :. b= -3`
or `f(x)=2x-3`
Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    CENGAGE ENGLISH|Exercise CONCEPT APPLICATION EXERCISE 1.15|8 Videos

  • RELATIONS AND FUNCTIONS

    CENGAGE ENGLISH|Exercise Single Correct Answer Type|125 Videos

  • RELATIONS AND FUNCTIONS

    CENGAGE ENGLISH|Exercise CONCEPT APPLICATION EXERCISE 1.13|7 Videos

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE ENGLISH|Exercise Archives (Numerical Value Type)|3 Videos

  • SCALER TRIPLE PRODUCTS

    CENGAGE ENGLISH|Exercise DPP 2.3|11 Videos

Similar Questions

Explore conceptually related problems

Find the domain of the function f(x) =(x^2-3x+5)/(x^2-5x+4) .

f: RrarrR ,f(x^2+x+3)+2f(x^2-3x+5)=6x^2-10 x+17AAx in R , then find the function f(x)dot

Range of the function f(x)=(x^2-3x+2)/(x^2+x-6) is

The range of the function f(x) = 3x^2+7x+10 is

Find the intervals of monotonicity of the following functions. (i) f(x) =-x^(3) +6x^(2)-gx-2 (ii) f(x) =x+(1)/(x+1) (iii) f(x) =x. e^(x-x^(2)) (iv) f(x) =x- cosx

Show that the function f(x) = x^3– 3x^2 + 6x – 100 is increasing on R

Find the period of the following functions (i) f(x)=|sin 3x| (ii) f(x)=2"cosec"(5x-6)+7 (iii) f(x) =x-[x-2.6], where [.] represents the greatest integer function.

Find the interval where the function f(x) 10 -x^3+6x^2-9x increases with x.

Consider the function f(x)=(x^(3)-x)|x^(2)-6x+5|, AA x in R , then f(x) is

A function f(x) is defined as f(x) = -6x^(2) . What is f(-3) ?