Question

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

Find f(g(x))

Answer 1

`2x^(2) -3x-12`

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`

Answer 2

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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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