Question

For each pair of functions \(f\) and \(g\) below, find \(f(g(x))\) and \(g(f(x))\). Then, determine whether \(f\) and \(g\) are inverses of each other. Simplify your answers as much as possible. (Assume that your expressions are defined for all \(x\) in the domain of the composition. You do not have to indicate the domain.) (a) \(f(x) = \frac{x+7}{2}\) \(g(x) = 2x - 7\) \(f(g(x)) = \square\) \(g(f(x)) = \square\) \(\circ f\) and \(g\) are inverses of each other \(\circ f\) and \(g\) are not inverses of each other (b) \(f(x) = 3x\) \(g(x) = 3x\) \(f(g(x)) = \square\) \(g(f(x)) = \square\) \(\circ f\) and \(g\) are inverses of each other \(\circ f\) and \(g\) are not inverses of each other

          For each pair of functions \(f\) and \(g\) below, find \(f(g(x))\) and \(g(f(x))\).
Then, determine whether \(f\) and \(g\) are inverses of each other.
Simplify your answers as much as possible.
(Assume that your expressions are defined for all \(x\) in the domain of the composition.
You do not have to indicate the domain.)
(a) \(f(x) = \frac{x+7}{2}\)
\(g(x) = 2x - 7\)
\(f(g(x)) = \square\)
\(g(f(x)) = \square\)
\(\circ f\) and \(g\) are inverses of each other
\(\circ f\) and \(g\) are not inverses of each other
(b) \(f(x) = 3x\)
\(g(x) = 3x\)
\(f(g(x)) = \square\)
\(g(f(x)) = \square\)
\(\circ f\) and \(g\) are inverses of each other
\(\circ f\) and \(g\) are not inverses of each other

For each pair of functions f and g below, find f(g(x)) and g(f(x)).
Then, determine whether f and g are inverses of each other.
Simplify your answers as much as possible.
(Assume that your expressions are defined for all x in the domain of the composition.
You do not have to indicate the domain.)
(a) f(x) = (x+7)/(2)
g(x) = 2x - 7
f(g(x)) = □
g(f(x)) = □
∘ f and g are inverses of each other
∘ f and g are not inverses of each other
(b) f(x) = 3x
g(x) = 3x
f(g(x)) = □
g(f(x)) = □
∘ f and g are inverses of each other
∘ f and g are not inverses of each other

Added by Christina W.

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