Answer:
(f∘g)(x) = 12x² - 12x + 8
Step-by-step explanation:
f(x) = 3x²+5 and g(x) = 2x - 1
we want to find (f°g)(x) which is the same as saying f(g(x))
This essentially is saying f composition g which means to copy down the f(x) equation but wherever x is plug in the equation g(x)
so first we copy down f(x)
3x²+5
we then plug in g(x) where x is
3(2x-1)² + 5
we now simplify
3(2x-1)² is the same as saying 3(2x - 1 ) ( 2x - 1 )
3(2x - 1 ) ( 2x - 1 ) + 5
simplify using FOIL
Multiply the Fronts 2x * 2x = 4x²
Multiply the Outers -1 * -1 = 1
Multiply the Inners 2x * -1 = -2x
Multiply the Lasts 2x * -1 = -2x
we then add everything back into parenthesis
3 * (4x^2 - 4x + 1 ) + 5
finally we distribute
4x² * 3 = 12x² , -4x * 3 = -12x and 1 * 3 = 3
12x² - 12x + 3
finally we add the 5
12x² - 12x + 8
and we are done!
