express your answer as a polynomial in standard form.\n$f(x) = -2x - 11$\n$g(x) = x^2 + 3x - 7$\nfind…

express your answer as a polynomial in standard form.\n$f(x) = -2x - 11$\n$g(x) = x^2 + 3x - 7$\nfind: $f(g(x))$

express your answer as a polynomial in standard form.\n$f(x) = -2x - 11$\n$g(x) = x^2 + 3x - 7$\nfind: $f(g(x))$

Answer

Explanation:

Step1: Substitute ( g(x) ) into ( f(x) )

We know that ( f(x) = -2x - 11 ) and ( g(x) = x^2 + 3x - 7 ). To find ( f(g(x)) ), we substitute ( g(x) ) in place of ( x ) in ( f(x) ). So we get ( f(g(x)) = -2(x^2 + 3x - 7) - 11 ).

Step2: Distribute the -2

Using the distributive property ( a(b + c + d)=ab+ac+ad ), we distribute -2 across ( x^2 + 3x - 7 ). So ( -2(x^2 + 3x - 7)=-2x^2-6x + 14 ). Now our expression becomes ( -2x^2 - 6x + 14 - 11 ).

Step3: Combine like terms

We combine the constant terms 14 and -11. ( 14-11 = 3 ). So the simplified expression is ( -2x^2 - 6x + 3 ).

Answer:

( -2x^2 - 6x + 3 )