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The functions f and g are such that
f(x) = 3x - 1

g(x)=x² +4

Given that fg(x) = 2gf(x),
show that 15x² - 12x-1=0

The functions f and g are such that fx 3x 1 gxx 4 Given that fgx 2gfx show that 15x 12x10 class=

Respuesta :

Answer:

see explanation

Step-by-step explanation:

to find f(g(x) substitute x = g(x) into f(x)

f(g(x)

= f(x² + 4)

= 3(x² + 4) - 1

= 3x² + 12 - 1

= 3x² + 11

---------------

to find g(f(x) , substitute x = f(x) into g(x)

g(f(x)

= g(3x - 1)

= (3x - 1)²  + 4 ← expand (3x - 1)² using FOIL

= 9x² - 6x + 1 + 4

= 9x² - 6x + 5

--------------------

given that

f(g(x) = 2g(f(x) , that is

3x² + 11 = 2(9x² - 6x + 5) ← distribute parenthesis

3x² + 11 = 18x² - 12x + 10 ( subtract 3x² from both sides )

11 = 15x² - 12x + 10 ( subtract 11 from both sides )

0 = 15x² - 12x - 1

Then it is shown that

15x² - 12x - 1 = 0

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