Question

If fof(x)=4x-9, find f(x), where f(x) is a linear function

Answer 1

SOLUTION

GIVEN

$\sf{f \circ f(x) = 4x - 9}$

Where f(x) is a linear function

TO DETERMINE

The function f(x)

EVALUATION

Here it is given that f(x) is a linear function

Let f(x) = ax + b

$\sf{f \circ f(x) }$

$\sf{ = f ( f(x)) }$

$\sf{ = f (ax + b) }$

$\sf{ = a(ax + b) + b}$

$\sf{ = {a}^{2} x + ab + b}$

Now

$\sf{f \circ f(x) = 4x - 9} \: \: \: gives$

$\sf{ \implies \: {a}^{2} x + ab + b = 4x - 9}$

$\sf{ \implies \: {a}^{2} = 4 \: \: \: and \: \: ab + b = - 9}$

Now

$\sf{ {a}^{2} = 4 \: \: \: gives \: \: a \: = \pm \: 2}$

Again a = 2 & ab + b = - 9 gives

b = - 3

Again a = - 2 & ab + b = - 9 gives

b = 9

Hence the required function

• f(x) = 2x - 3

• f(x) = - 2x + 9

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Answer 2

Step-by-step explanation:

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