For the given functions f and g , find the indicated composition.
f(x) = -5x + 6, g(x) = 2x + 5
(g.f)(x)
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Assuming you mean (g * f)(x)
(g * f)(x) is the same as g(x)*f(x)
So we multiply the functions to get
g(x)*f(x) = (2x + 5)*(-5x + 6)
g(x)*f(x) = 2x*(-5x + 6) + 5*(-5x + 6)
g(x)*f(x) = 2x*(-5x) + 2x*(6) + 5*(-5x) + 5*(6)
g(x)*f(x) = -10x^2 + 12x - 25x + 30
g(x)*f(x) = -10x^2 - 13x + 30
(g * f)(x) = -10x^2 - 13x + 30
The final answer is (g * f)(x) = -10x^2 - 13x + 30