Question

what is the value of c which lies in [1,2] for the function f(x) = 4x and g(x) = 3x2

Answer 1

Answer:

step by step explanation

Answer 2

SOLUTION

TO DETERMINE

The value of x which lies in [1,2] for the function f(x) = 4x and g(x) = 3x² are equal

EVALUATION

Here the given two functions are

f(x) = 4x and g(x) = 3x²

So by the given condition

f(x) = g(x)

$\sf{ \implies 4x = 3 {x}^{2} }$

$\sf{ \implies 3 {x}^{2} = 4x}$

$\sf{ \implies 3 {x}^{2} - 4x = 0}$

$\sf{ \implies x(3x - 4)= 0}$

$\displaystyle \: \sf{ \implies x= 0, \frac{4}{3} [, ] }$

Now

$\displaystyle \: \sf{ 0 \notin [1, 2] }$

But

$\displaystyle \: \sf{ \frac{4}{3} \in [1, 2] }$

So the required value is

$\displaystyle \: \sf{ \frac{4}{3} }$

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