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If f(x)=3x²+5 and g(x)=2x−1, find (f∘g)(x)

BRAINLIEST

Sagot :

Fieryanswererftidn

Answer:

(f∘g)(x) = 12x²-12x+8

Explanation:

  • f(x)=3x²+5 and g(x)=2x−1, find fg(x)

fg(x)

f(2x−1)

3(2x−1)²+5

3(4x²-2 * 1 *2x + 1) + 5

3(4x²-4x + 1) +5

12x²- 12x + 3 + 5

12x²-12x+8

SenorMathWizidn

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!

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