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If f(x)= px+q and f(f(f(x)))=8x+21 and if p and q are real #'s, then p+q equals...
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High School Teacher
Given `f(x)= px + q`
`` First, we will find `f(f(x)). `
`==gt f(f(x))= f(px+q) = p(px+q) +q = p^2 x+ pq+q`
`` Now we will find `f(f(f(x)))= f(p^2 x + pq+q) `
`==gt f(p^2x + pq+q)= p(p^2x+pq+q) +q = p^3 x + p^2q +pq+q `
`==gt f(f(f(x)))= p^3 x + p^2 q+pq +q= 8x+ 21`
`` Now we will compare sides.
`==gt (p^3) x + (p^2q + pq +q) = 8x + 21 `
`==gt p^3 = 8 ==gt p= 2 `
`==gt p^2q + pq + q = 21`
`` But `p= 2 `
`==gt 4q + 2q + q = 21 `
`==gt 7q = 21 `
`==gt q= 21/7= 3 `
`==gt p= 2 and q= 3 `
`==gt p+q = 2+3 = 5`
`` Then the answer is c) 5
Posted by hala718 on December 13, 2011 at 11:50 AM (Answer #1)
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