Answer:
f(g(x)) = -5x^2 - 30x + 49
Step-by-step explanation:
f(g(x)) is a composite function, where 'x' in f(x) is replaced by 'x^2 + 6x - 7' because the latter expression is now the input to f(x).
Write out f(x) = -5x + 14, and then replace each 'x' with '( )'
f( ) = -5( ) + 14
Now insert 'g(x)' into the first set of parentheses and 'x^2 + 6x - 7' into the second set of parentheses:
f( ) = -5( ) + 14 becomes:
f(g(x) = -5(x^2 + 6x - 7) + 14. After simpification, this becomes
f(g(x)) = -5x^2 - 30x + 35 + 14, or
f(g(x)) = -5x^2 - 30x + 49
