Function f and g are defined by
f:x→4-x and g:x→px^2+q where p and q are constants.Given that the composite function gf:x→x^2-8x+11,find
the values of p and q.

1. 👍 0
2. 👎 0
3. 👁 157
1. f(x) = 4-x
g(x) = px^2 + q

g(f(x))
= g(4-x)
= p(4-x)^2 + q
= p(16 - 8x + x^2) + q
= px^2 - 8p x + 16p+q

if px^2 - 8p x + 16p+q = x^2 - 8x + 11

then p = 1
16p+q = 11
16 + q = 11
q = -5

and -8p = -8
p = 1, which checks out

1. 👍 0
2. 👎 0
posted by Reiny

## Similar Questions

1. ### Calculus

A cubic polynomial function f is defined by f(x) = 4x^3 + ax^2 + bx + k? A cubic polynomial function f is defined by: f(x) = 4x^3 + ax^2 + bx + k where a, b, and k are constants. The function f has a local minimum at x= -1, and

asked by Leanna on February 8, 2011
2. ### Calculus

A cubic polynomial function f is defined by f(x) = 4x^3 + ax^2 + bx + k? A cubic polynomial function f is defined by: f(x) = 4x^3 + ax^2 + bx + k where a, b, and k are constants. The function f has a local minimum at x= -1, and

asked by Leanna on February 9, 2011
3. ### calculus

A cubic polynomial function f is defined by f(x)= 4x^3+ab^2+bx+k where a, b, k, are constants. The function f has a local minimum at x=-2 A. Fine the vales of a and b B. If you integrate f(x) dx =32 from o to 1, what is the value

4. ### College Algebra

Let g(x) = -2x2 + bx + c be a quadratic function, defined everywhere, where b and c are constants. If x = 1 marks the location of one of the zeros of this quadratic function, and if the y-intercept of this function is at (0, 5),

asked by Brianna on September 26, 2011
5. ### college Algebra

Let g(x) = -2x2 + bx + c be a quadratic function, defined everywhere, where b and c are constants. If x = 1 marks the location of one of the zeros of this quadratic function, and if the y-intercept of this function is at (0, 5),

asked by Brianna on September 26, 2011
6. ### calculus

Let f be the function defined by f(x)= sqrt(x), 0

asked by lisa on October 8, 2012
7. ### Calculous

let f be the function defined by |x-1|+2 for Xor equal to 1. where a and b are constants a)if a=2 and b=3 is f continious for all x? justify your answer b)describe all the values of a and b for which f is a continious function c)

asked by Yoona on November 21, 2011
8. ### AP Calculous

let f be the function defined by |x-1|+2 for Xor equal to 1. where a and b are constants a)if a=2 and b=3 is f continious for all x? justify your answer b)describe all the values of a and b for which f is a continious function c)

asked by Yoona on November 21, 2011
9. ### calculus

i'm having trouble with a problem in my calc class...it isn't really calculus yet since we're still in the review section but it goes somethign like this: ( don't have it in front of me) a rational function is defined by: R/(x-K)

asked by Rob on March 15, 2007
10. ### math

express y=0.1(1000)^x in the form lg y =mx+c ,where m and c are constants ,and x is a function of x . Determine the constants m and c and the function x .

asked by Kris on July 18, 2013

More Similar Questions