Answered

for f(x)=x+3 and g(x)=4x+5 find the following functions(simplify answers)

(fg)(x)=


(gf)(x)=


(f*g)(-1)=

Verified Answer :

Panoyin

\((f * g)(x) = (x + 3)(4x + 5) \\(f * g)(x) = x(4x + 5) + 3(4x + 5) \\(f * g)(x) = x(4x) + x(5) + 3(4x) + 3(5) \\(f * g)(x) = 4x^{2} + 5x + 12x + 15 \\(f * g)(x) = 4x^{2} + 17x + 15\)

\((g * f)(x) = (4x + 5)(x + 3) \\(g * f)(x) = 4x(x + 3) + 5(x + 3) \\(g * f)(x) = 4x(x) + 4x(3) + 5x(x) + 5(3) \\(g * f)(x) = 4x^{2} + 12x + 5x + 15 \\(g * f)(x) = 4x^{2} + 17x + 15\)

\((f * g)(-1) = (-1 + 3)(4(-1) + 5) \\(f * g)(-1) = (2)(-4 + 5) \\(f * g)(-1) = (2)(1) \\(f * g)(-1) = 2\)

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