contestada

the functions f and g are such that
f(x)=4x-1 and g(x)=x²+3

a) find f^-1 (x)

b) if we are told that fg(x) = 2gf(x) we can show that
ax²-bx-3=0
where a and b are integers.
work out the value of a and the value of b.

Respuesta :

Answer:

a) [tex]f(x)^-1=(x+1)/4\\\\[/tex]

b) a=28 ; b=-16

Step-by-step explanation:

*For b only:

We know that

[tex]fg(x)---> 4(x^2+3)-1\\2gf(x)---> 2[(4x-1)^2+3]\\\\[/tex]

From this we create an equation

[tex]4(x^2+3)-1= 2[(4x-1)^2+3][/tex]

We solve the equation

[tex]4x^2+11=32x^2-16x+8\\4x^2+11-32x^2+16x-8=0\\28x^2-16-3=0[/tex]

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