Question

F(x) = 2x - 3 and f(x) = f'(x), find the value of x.​

Answer 1

x=1

Explanation:

According to your typed question,

f(x)=2x-3

Let f(x)=y

y=2x-3

Now,

Interchanging the positions of x and y

x=2y-3

x+3=2y

x+3/2=y

f'(x)=x+3/2

Then,

f(x)=f'(x)

2x-3=x+3/2

2(2x-3)=x+3

4x-3=x+3

4x-x=3+3

3x=3

x=3/3

x=1

According to your image question,

f(x)=x/2x-3

f(x)=f'(x)

Now,

Let y=f(x)

y=x/2x-3

y(2x-3)=x

2xy-3=x

2xy-x=3

x(2y-1)=3

2y-1=3x

2y=3x+1

y=3x+1/2

f'(x)=3x+1/2

Then,

f(x)=f'(x)

x/2x-3=3x+1/2

2x=6xsq+2x-9x+3

2x=6xsq+7x+3

solve for x ok