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

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

Explanation:

`$ f(x) = x - 3 $$$$ g(x) = x + (7)/(2) $$\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 + (7)/(2) $ \\\textup{Simplifying this we get:}\\\textbf{$$g(f(x)) = (2x + 1)/(2)$$}`