let f(x)=ax+b where a and b are integers. If f(f(0))=0 and f(f(f(4)))=9 then the value of f(f(f(f(10)))) is equal to
Answers
Answer:
The correct answer to this question is
f(f(f(f(10)))) = 10
f(f(f(f(10)))) =
Step-by-step explanation:
Given f(x) = ax+b
Now,
f(f(0)) = 0
f(a(0) + b) = 0
f(b) = 0
a(b) + b = 0
ab + b = 0 (equation 1 )
b*(a+1) = 0
b = 0 (or) a = -1
Now,
f(f(f(4))) = 9
f(f(a(4) + b)) = 9
f(f(4a + b)) = 9
f(a(4a + b) + b) = 9
f(4a² + ab + b) = 9 from equation 1
f(4a²) = 9
a(4a²) + b = 9
4a³ + b = 9 (equation 2)
solving equation 1 and 2
if a = -1
then 4*(-1)³ + b = 9
-4 + b = 9
b = 13
if b = 0
then 4a³ + 0 = 9
a³ = 9/4
Now,
f(f(f(f(10)))) = f(f(f(a(10) + b)))
= f(f(f(10a + b)))
= f(f(a(10a + b) + b))
= f(f(10a² + ab +b)) from equation 1
= f(f(10a²))
= f(a(10a²) + b)
= f(10a³ + b)
= a(10a³ + b) + b
= 10a⁴ + ab + b from equation 1
= 10a⁴
f(f(f(f(10)))) = 10a⁴
if a = -1
f(f(f(f(10)))) = 10a⁴ = 10 * (-1)⁴ = 10 * 1 = 10
f(f(f(f(10)))) = 10
if
f(f(f(f(10)))) = 10a⁴ =
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