Question

For the functions f(x) = x − 3 and g\left(x\right)=\frac{x+7}{2} g ( x ) = x + 7 2 , find [g∘f](x). Group of answer choices \frac{x^2+4x-21}{2} x 2 + 4 x − 21 2 \frac{3x+1}{2} 3 x + 1 2 \frac{x+4}{2} x + 4 2 \frac{x+1}{2}

Answer 1

Answer:

$\textbf{ g(f(x)) = \frac{2x + 1}{2} }$

Step-by-step explanation:

$f(x) = x - 3 g(x) = x + \frac{7}{2} \textup{To compute g(f(x))} \implies g(f(x)) = g(x - 3) \\\textup{i.e., to substitute x - 3 instead of x in g(x)}\\ \therefore g(x - 3) = x - 3 + \frac{7}{2} \\\textup{Simplifying this we get:}\\\textbf{ g(f(x)) = \frac{2x + 1}{2} }$