Finding value of k for which f g ( x ) = k has equal roots?I've been going through this community and I Find this really helpful. About me(I know I should be precise but ya), I'm just a highschool student who can't afford any coachings/schools. Self schooling being my only option I'm trying to teach myself mathematics from some torrented books. I am on functions and their graphs and stuck with one questionThe functions f and g are defined for x ∈ R by f ( x ) = 4 x − 2 x 2 ; g ( x ) = 5 x + 3.(i) Find the range of f. (ii) Find the value of the constant k for which the equation g f ( x ) = k has equal roots.Now, I do understand the composition of functions but I just don't understand what they are asking in this case, g ( f x ( ) = k would result in 20 x − 10 x 2 + 3 = kNow this is a quadratic equation of second degree which should have 2 roots/solutions, but that's the case if the right hand side was zero and not k. I have absolutely no idea how to tackle this question and what's being asked in part ii of the question. Anyhelp would be highly appreciated

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Finding value of k for which   f  g  (  x  )  =  k has equal roots?I&#039;ve been going through this community and I Find this really helpful. About me(I know I should be precise but ya), I&#039;m just a highschool student who can&#039;t afford any coachings/schools. Self schooling being my only option I&#039;m trying to teach myself mathematics from some torrented books. I am on functions and their graphs and stuck with one questionThe functions f and g are defined for   x  ∈  R by   f  (  x  )  =  4  x  −  2      x    2    ;  g  (  x  )  =  5  x  +  3.(i) Find the range of f. (ii)  Find the value of the constant k for which the equation   g  f  (  x  )  =  k has equal roots.Now, I do understand the composition of functions but I just don&#039;t understand what they are asking in this case,   g  (  f  x  (  )  =  k would result in  20  x  −  10      x    2    +  3  =  kNow this is a quadratic equation of second degree which should have 2 roots/solutions, but that&#039;s the case if the right hand side was zero and not k. I have absolutely no idea how to tackle this question and what&#039;s being asked in part ii of the question. Anyhelp would be highly appreciated

Waldruhylm · Accepted Answer

Step 1Your equation could be rewritten as  10      x    2    −  20  x  +  (  k  −  3  )  =  0.Step 2Recall that the roots of a quadratic equation   a      x    2    +  b  x  +  c  =  0 are given by            −      b      ±                        b          2                −        4        a        c                    2      a        .So the two roots are equal when       b    2    −  4  a  c  =  0.

Finding value of k for which fg(x)=k has equal roots?

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