Question

F(x) = 2x^2-7x-7 g(x) = x+1 Find f(g(x))

Answer 1

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$f(x) = 2 {x}^{2} - 7x - 7$

$g(x) = x + 1$

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$f(g(x)) = 2 ({x + 1})^{2} - 7(x + 1) - 7$

$f(g(x)) = 2( {x}^{2} + 2x + 1) - 7x - 7 - 7$

$f(g(x)) = 2 {x}^{2} + 4x + 2 - 7x - 7 - 7$

Collect like terms

$f(g(x)) = 2 {x}^{2} + (4 - 7)x - 14 + 2$

$f(g(x)) = 2 {x}^{2} - 3x - 12$

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Answer 2

Answer:

$2x^{2} -3x-12$

Step-by-step explanation:

To solve composite functions, figure out which function is on the "inside" and the outside":

f(x) is the inside and g(x) is the outside

Now plug the value of g(x) into the x values of f(x):

$2(x+1)^{2}-7(x+1)-7$

Then distribute following the steps of PEMDAS:

$2(x^{2}+2x+1)-7x-7-7$

$2x^{2} + 4x + 2 - 7x -14$

Then combine like terms:

$2x^{2} -3x-12$