Math, asked by amanjos901, 1 day ago

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

Answered by akansha804
3

Answer:

The correct answer to this question is

f(f(f(f(10)))) = 10

f(f(f(f(10)))) = 10 *(9/4)^{4/3}

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

a = (9/4)^{1/3}

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 a = (9/4)^{1/3}

f(f(f(f(10)))) = 10a⁴ = 10 * ((9/4)^{1/3})^{4} = 10 *(9/4)^{4/3}

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