Question

if f(x) = 5x + 2 and g(x) = x + 3, find (f ∘ g)(x) and (g ∘ f)(x).
(f ∘ g)(x) = 5x + 17
(g ∘ f)(x) = \square

Explanation:

Step1: Recall the definition of function composition

The composition \((g \circ f)(x)\) means \(g(f(x))\). So we need to substitute \(f(x)\) into \(g(x)\).

Step2: Substitute \(f(x)\) into \(g(x)\)

We know that \(f(x)=5x + 2\) and \(g(x)=x + 3\). Substitute \(f(x)\) (which is \(5x + 2\)) in place of \(x\) in \(g(x)\). So we get \(g(f(x))=g(5x + 2)\).

Step3: Evaluate \(g(5x + 2)\)

Since \(g(x)=x + 3\), then \(g(5x + 2)=(5x + 2)+3\).

Step4: Simplify the expression

Simplify \((5x + 2)+3\) by combining like terms. \(2 + 3 = 5\), so the result is \(5x+5\).

Answer:

\(5x + 5\)